Gait analysis method and gait analysis system

ABSTRACT

A triaxial acceleration sensor and a triaxial angular rate sensor are mounted on each of the lower limb portions on both sides of one joint among joints constituting a part of one lower limb of a subject. The acceleration and angular rate of each lower limb portion are measured by the triaxial acceleration sensor and triaxial angular rate sensor while the subject is walking. The orientations of each lower limb portion while walking are calculated on the basis of the measured acceleration and angular rate. A three-dimensional model including the motion trajectory of one joint is constructed by linking the lower limb portions in the calculated orientation to each other. The angle formed by the acceleration vector of one joint when the heel strikes the ground to the movement trajectory in the sagittal plane is calculated as a gait parameter.

TECHNICAL FIELD

The present invention relates to a gait analysis method and a gaitanalysis system using a body-worn sensor (also referred to as a“wearable sensor”), and particularly to a gait analysis method and agait analysis system for calculating novel gait parameters useful forassessment of gait action.

BACKGROUND ART

Measurement of gait action is used to assess gait abilities, to plantreatments, and to assess treatments in a quantitative manner.Conventionally, examples of general systems for gait measurement with aninstrument include an optical three-dimensional motion analysis system.The measurement environment is subject to restrictions, generallyrequiring a long time for analysis. Therefore, the opticalthree-dimensional motion analysis system is only used in the area ofresearch, and it is difficult to say that the optical three-dimensionalmotion analysis system has been in clinical use sufficiently.

In recent years, development and research of a gait measurement systemcapable of easier measurement has drawn attention. In the past, gaitmeasurement using an acceleration sensor attached to a human body wasproposed by Morris (Non-Patent Literature 1). Since then, measurementmethods using a small-sized sensor, e.g., an acceleration sensor or anangular velocity sensor, have been researched (Non-Patent Literature 1to 3). Thus, restrictions on measurement environments and a longrequired time, which were the problems with the conventional system,have been overcome, and it can be said that the practicability inclinical use has been increased.

However, most of the reports about sensor systems such as thosedescribed above indicate a mere acceleration comparison ortwo-dimensional gait measurement in which gait is recognized as a planemotion. A three-dimensional gait measurement system using a small-sizedsensor has not been achieved.

Given the above, the inventors of the present application have pursuedthe development of a three-dimensional gait analysis using anacceleration sensor and an angular velocity sensor (Non-PatentLiterature 4 and 5). As a result, the inventors of the presentapplication have succeeded to measure a three-dimensional motionconsidering rotation of a joint with high precision by means of ananalysis method using quaternion calculation (Non-Patent Literature 6).

CITATION LIST Non-Patent Literature

Non-Patent Literature 1: Morris, J. R. W.; Accelerometry—a technique forthe measurement of human body movements, Journal of Biomechanics 6,729-736, (1973)

Non-Patent Literature 2: Tao Liu, Yoshio Inoue, Kyoko Shibata:Development of a wearable sensor system for quantitative gait analysis,Measurement, Volume 42, Issue 7, 978-988, (2009)

Non-Patent Literature 3: Pietro Picerno, Andrea Cereatti, AurelioCappozzo: Joint kinematics estimate using wearable inertial and magneticsensing modulues, Gait & Posture 28, 588-595, (2008)

Non-Patent Literature 4: Ryo Takeda, Shigeru Tadano, Masahiro Todoh,Manabu Morikawa, Minoru Nakayasu, Satoshi Yoshinari: Gait analysis usinggravitational acceleration measured by wearable sensors, Journal ofBiomechanics, Volume 42, Issue 3, 223-233, (2009)

Non-Patent Literature 5: Ryo Takeda, Shigeru Tadano, Akiko Natorigawa,Masahiro Todoh, Satoshi Yoshinari: Gait posture estimation usingwearable acceleration and gyro sensors, Journal of Biomechanics, Volume42, Issue 15, 2486-2494, (2009)

Non-Patent Literature 6: Hiroaki Miyagawa, Ryo Takeda, ShigeruTadano:Kasokudo-Kakusokudo Sensa Ni Yoru Sanjigen Hoko Kaiseki(Three-dimensional gait analysis using acceleration and angular velocitysensors), Proceedings of the Japan Society of Mechanical Engineersannular meeting of 2010, Vol. 5: 63-64, 2010

SUMMARY OF INVENTION Technical Problem

It is an object of the present invention to develop the conventionalthree-dimensional gait analysis using an acceleration sensor and anangular velocity sensor to provide a gait analysis method and a gaitanalysis system that can obtain novel gait parameters useful forassessment of gait actions of a subject.

Solution to Problem

The present invention solves the aforementioned problem, and a gaitanalysis method of the present invention is characterized in that atri-axial acceleration sensor and a tri-axial angular velocity sensorare attached to lower limb portions across at least one joint of jointsconstituting at least one of lower limbs of a subject, acceleration andangular velocity of each lower limb portion are respectively measuredwith the tri-axial acceleration sensor and the tri-axial angularvelocity sensor during gait of the subject, the posture of each lowerlimb portion during the gait is calculated on the basis of theacceleration and the angular velocity measured, the lower limb portionsin the calculated posture are coupled to one another to construct athree-dimensional model including a motion trajectory of the at leastone joint, and an angle of an acceleration vector of the at least onejoint at the time of heel contact with regard to the motion trajectoryin a sagittal plane is calculated as a gait parameter.

A gait analysis system of the present invention is characterized byincluding a tri-axial acceleration sensor and a tri-axial angularvelocity sensor attached to lower limb portions across at least onejoint of joints constituting at least one of lower limbs of a subject torespectively measure acceleration and angular velocity of each lowerlimb portion during gait of the subject, a model construction means forcalculating the posture of each lower limb portion during the gait onthe basis of the acceleration and the angular velocity measured andconstructing a three-dimensional model including a motion trajectory ofthe at least one joint by coupling the lower limb portions in thecalculated posture to one another, and a gait parameter calculationmeans for calculating an angle of an acceleration vector of the at leastone joint at the time of heel contact with regard to the motiontrajectory in a sagittal plane as a gait parameter.

Advantageous Effect of Invention

With the gait analysis method and the gait analysis system according tothe present invention, a three-dimensional model including a motiontrajectory of at least one joint is constructed on the basis ofacceleration data and angular velocity data of each lower limb portionduring gait of a subject, and an angle formed by the motion trajectoryand an acceleration vector of a joint at the time of heel contact iscalculated, enabling determination of novel gait parameters useful forgait analysis.

In the gait analysis method of the present invention, the at least onejoint may be a knee joint.

In addition, in the gait analysis method of the present invention, thethree-dimensional model including the motion trajectory of at least onejoint maybe constructed with respect to each of right and left lowerlimbs of the subject.

Furthermore, in the gait analysis method of the present invention,approximation straight lines may be formed with respect to the motiontrajectories of right and left joints in a horizontal plane, and anangle formed between the approximation straight lines may be calculatedas a gait parameter.

Furthermore, in the gait analysis method of the present invention, aLissajous figure of a joint may be created from a three-dimensionalmodel, and a gait parameter may be calculated on the basis of theLissajous figure.

In addition, the gait analysis system of the present invention may beconfigured such that the tri-axial acceleration sensor and the tri-axialacceleration sensor are attached to the right and left lower limbs of asubject, the gait parameter calculation means forms approximationstraight lines with respect to the motion trajectories of the right andleft joints in a horizontal plane, and calculates an angle formedbetween the approximation straight lines as a gait parameter.

Furthermore, the gait analysis system of the present invention may beconfigured such that the parameter calculation means creates a Lissajousfigure of a joint from a three-dimensional model and calculates a gaitparameter on the basis of the Lissajous figure.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a view describing fundamental planes of a body motion.

FIG. 2 is a view illustrating a direction of flexion and extensionmotions and a range of motion of a hip joint.

FIG. 3 is a view illustrating a direction of adduction and abductionmotions and a range of motion of a hip joint.

FIG. 4 is a view illustrating a direction of internal rotation andexternal rotation motions and a range of motion of a hip joint.

FIG. 5 is a view illustrating a direction of flexion and extensionmotions and a range of motion of a knee joint.

FIG. 6 is a view illustrating a direction of plantar flexion and dorsiflexion and a range of motion of an ankle joint.

FIG. 7 is a view illustrating a direction of adduction and abduction anda range of motion of an ankle joint.

FIGS. 8(a) and (b) are views describing a method of expressing anorientation of an ordinate system of a three-dimensional space.

FIG. 9 is a view illustrating two coordinate systems in athree-dimensional space.

FIG. 10 is a view describing general Euler angles.

FIG. 11 is a block configurational diagram of a processing device of agait analysis system according to an embodiment of the presentinvention.

FIG. 12 is views illustrating a sensor attachment arrangement of a gaitanalysis system according to the aforementioned embodiment and a gaitanalysis method according to an embodiment of the present inventionusing the same, FIG. 12(a) is a front view, and FIG. 12(b) is a rearview.

FIG. 13 is a view describing a wire-frame model of lower limbs accordingto the aforementioned embodiment.

FIG. 14 is views describing a sensor coordinate system, a groundcoordinate system, and a segment coordinate system according to theaforementioned embodiment, FIG. 14(a) is a side view, and FIG. 14(b) isa front view.

FIG. 15 illustrates a definition of a coordinate system of a right thighsegment according to the aforementioned embodiment, FIG. 15(a) is asideview, and FIG. 15(b) is a front view.

FIG. 16 illustrates a definition of a coordinate system of a right shanksegment according to the aforementioned embodiment, FIG. 16(a) is asideview, and FIG. 16(b) is a front view.

FIG. 17 is a diagram illustrating an analysis flow according to the gaitanalysis system and the gait analysis method according to theaforementioned embodiment.

FIG. 18 is a view describing a principle of calculating an initialposture (initial orientation) of a sensor from acceleration data.

FIG. 19 is a view illustrating a seated posture for measurement ofacceleration data at rest.

FIG. 20 is views illustrating two gravitational acceleration vectors foruse in defining a sensor coordinate system.

FIG. 21 is graphs illustrating states before and after low-pass filterprocessing with respect to data obtained from an angular velocitysensor, the upper illustrates a state before the processing, and thelower illustrates a state after the processing.

FIG. 22 is a graph illustrating a gyro bias included in data obtainedfrom an angular velocity sensor.

FIG. 23 is a graph illustrating a change of an angular velocity of ashank during gait.

FIG. 24 is a graph illustrating a distance in a walking direction froman original point (midpoint of right and left hip joint centers) to aright toe.

FIG. 25 is a view illustrating motion trajectories of joints in asagittal plane and an acceleration vector at the time of heel contact.

FIG. 26 is a view illustrating motion trajectories of knee joints in ahorizontal plane and a trajectory angle of knee joints in a horizontalplane.

FIG. 27 is a flowchart indicating a data flow of a gait analysis systemaccording to the aforementioned embodiment.

FIG. 28 is a flowchart indicating a procedure of an experiment accordingto the gait analysis system and the gait analysis method according tothe aforementioned embodiment.

FIG. 29 is photographs illustrating a walkway employed in theaforementioned experiment, FIG. 29(a) is a straight flat way of 7 m, andFIG. 29(b) is a treadmill.

FIG. 30 is graphs illustrating results of measurement of gait of PatientA, FIG. 30(a) is a graph illustrating a knee flexion angle, FIG. 30(b)is a graph illustrating motion trajectories of joints (great trochanter,knee joint, ankle joint) of a right leg in a sagittal plane, FIG. 30(c)is a graph illustrating motion trajectories of joints (great trochanter,knee joint, ankle joint) of a left leg in a sagittal plane, and FIG.30(d) is a graph illustrating motion trajectories of knee joints in ahorizontal plane.

FIG. 31 is graphs illustrating results of measurement of a gait ofPatient B, FIG. 31(a) is a graph illustrating a knee flexion angle, FIG.31(b) is a graph illustrating motion trajectories of joints (greattrochanter, knee joint, ankle joint) of a right leg in a sagittal plane,FIG. 31(c) is a graph illustrating motion trajectories of joints (greattrochanter, knee joint, ankle joint) of a left leg in a sagittal plane,and FIG. 31(d) is a graph illustrating motion trajectories of kneejoints in a horizontal plane.

FIG. 32 is graphs illustrating results of measurement of gait of PatientC, FIG. 32(a) is a graph illustrating a knee flexion angle, FIG. 32(b)is a graph illustrating motion trajectories of joints (great trochanter,knee joint, ankle joint) of a right leg in a sagittal plane, FIG. 32(c)is a graph illustrating motion trajectories of joints (great trochanter,knee joint, ankle joint) of a left leg in a sagittal plane, and FIG.32(d) is a graph illustrating motion trajectories of knee joints in ahorizontal plane.

FIG. 33 is graphs illustrating results of measurement of gait of PatientD, FIG. 33(a) is a graph illustrating a knee flexion angle, FIG. 33(b)is a graph illustrating motion trajectories of joints (great trochanter,knee joint, ankle joint) of a right leg in a sagittal plane, FIG. 33(c)is a graph illustrating motion trajectories of joints (great trochanter,knee joint, ankle joint) of a left leg in a sagittal plane, and FIG.33(d) is a graph illustrating motion trajectories of knee joints in ahorizontal plane.

FIG. 34 is graphs illustrating results of measurement of gait of PatientE, FIG. 34(a) is a graph illustrating a knee flexion angle, FIG. 34(b)is a graph illustrating motion trajectories of joints (great trochanter,knee joint, ankle joint) of a right leg in a sagittal plane, FIG. 34(c)is a graph illustrating motion trajectories of joints (great trochanter,knee joint, ankle joint) of a left leg in a sagittal plane, and FIG.34(d) is a graph illustrating motion trajectories of knee joints in ahorizontal plane.

FIG. 35 is graphs illustrating results of measurement of gait of PatientF, FIG. 35(a) is a graph illustrating a knee flexion angle, FIG. 35(b)is a graph illustrating motion trajectories of joints (great trochanter,knee joint, ankle joint) of a right leg in a sagittal plane, FIG. 35(c)is a graph illustrating motion trajectories of joints (great trochanter,knee joint, ankle joint) of a left leg in a sagittal plane, and FIG.35(d) is a graph illustrating motion trajectories of knee joints in ahorizontal plane.

FIG. 36 is graphs illustrating results of measurement of gait of PatientG, FIG. 36(a) is a graph illustrating a knee flexion angle, FIG. 36(b)is a graph illustrating motion trajectories of joints (great trochanter,knee joint, ankle joint) of a right leg in a sagittal plane, FIG. 36(c)is a graph illustrating motion trajectories of joints (great trochanter,knee joint, ankle joint) of a left leg in a sagittal plane, and FIG.36(d) is a graph illustrating motion trajectories of knee joints in ahorizontal plane.

FIG. 37 is graphs illustrating results of measurement of gait of PatientH, FIG. 37(a) is a graph illustrating a knee flexion angle, FIG. 37(b)is a graph illustrating motion trajectories of joints (great trochanter,knee joint, ankle joint) of a right leg in a sagittal plane, FIG. 37(c)is a graph illustrating motion trajectories of joints (great trochanter,knee joint, ankle joint) of a left leg in a sagittal plane, and FIG.37(d) is a graph illustrating motion trajectories of knee joints in ahorizontal plane.

FIG. 38 is graphs illustrating results of measurement of gait of PatientI, FIG. 38(a) is a graph illustrating a knee flexion angle, FIG. 38(b)is a graph illustrating motion trajectories of joints (great trochanter,knee joint, ankle joint) of a right leg in a sagittal plane, FIG. 38(c)is a graph illustrating motion trajectories of joints (great trochanter,knee joint, ankle joint) of a left leg in a sagittal plane, and FIG.38(d) is a graph illustrating motion trajectories of knee joints in ahorizontal plane.

FIG. 39 is graphs illustrating results of measurement of gait of PatientJ, FIG. 39(a) is a graph illustrating a knee flexion angle, FIG. 39(b)is a graph illustrating motion trajectories of joints (great trochanter,knee joint, ankle joint) of a right leg in a sagittal plane, FIG. 39(c)is a graph illustrating motion trajectories of joints (great trochanter,knee joint, ankle joint) of a left leg in a sagittal plane, and FIG.39(d) is a graph illustrating motion trajectories of knee joints in ahorizontal plane.

FIGS. 40(a) to (h) are graphs illustrating motion trajectories of kneejoints of healthy persons in a horizontal plane.

FIGS. 41(a) to (h) are graphs illustrating motion trajectories of jointsof right legs of healthy persons in a sagittal plane and accelerationvectors at the time of heel contact.

DESCRIPTION OF EMBODIMENT

First, terms and technical terms regarding gait used herein aredescribed.

(1) Fundamental Planes of Body Motions

As illustrated in FIG. 1, there are three fundamental planes of a bodymotion as described below.

-   -   Horizontal plane

-   A plane dividing a body into upper and lower parts; also called a    transverse plane.    -   Coronal plane

-   A plane dividing a body into front and rear parts.    -   Sagittal plane

-   A plane dividing a body into right and left parts.

(2) Axes of Body Motions

When a body motion is rotation, the body motion can be expressed withreference to an axis, not a plane. This is defined as follows:

-   -   Median axis: A line segment common to a coronal plane and a        sagittal plane.    -   Frontal-horizontal axis: a line segment common to a coronal        plane and a horizontal plane.    -   Sagittal-horizontal axis: a line segment common to a sagittal        plane and a horizontal plane.

(3) Motions of Lower Limb Joints

A motion of a lower limb joint and an average range of motion of a jointof a healthy person are described. (3-1) Motions of hip joints

A hip joint is a three-degree-of-freedom joint that enables flexion andextension motions, adduction and abduction motions, and internalrotation and external rotation motions.

FIG. 2 illustrates a direction of flexion and extension motions and arange of motion of a hip joint. A direction in which a leg is swungforward is the flexion direction.

FIG. 3 illustrates a direction of adduction and abduction motions and arange of motion of a hip joint. It is a rotation in the coronal plane inwhich a direction in which a foot approaches the median axis is theadduction and a direction in which a foot moves away from the medianaxis is the abduction.

FIG. 4 illustrates a direction of internal rotation and externalrotation motions and a range of motion of a hip joint. It is a rotationabout an axis of a thigh. When a point is marked on a front surface ofthe thigh, a direction in which the point approaches the fundamentalsagittal plane is the internal rotation and a direction in which thepoint moves away from the fundamental sagittal plane is the externalrotation.

(3-2) Motions of Knee Joints

FIG. 5 illustrates a direction of flexion and extension and a range ofmotion. A direction in which a foot approaches buttocks is the flexiondirection and a direction in which a foot moves away from buttocks isthe extension direction. In the field of motion analysis, a knee jointis often considered a hinge joint. However, technically, the motion of aknee joint is not limited to flexion and extension, but the movablemotion can be expanded in the adduction and abduction directions or inthe internal rotation and external rotation directions due toimpairment, e.g., damage to an anterior cruciate ligament. In the fieldof orthopedic surgery, the motion of a knee joint is generally treatedthree-dimensionally. Therefore, according to the present invention, aknee joint is treated as a spheroidal joint. A direction in which a kneejoint has varus deformity (bowleg) is the adduction direction, and adirection in which a knee joint has valgus deformity (knock knee) is theabduction direction. A direction in which the front surface of a shankfaces inward relative to the thigh is the internal rotation direction,and a direction in which the front surface of a shank faces outward isthe external rotation direction.

(3-3) Motions of Ankle Joints

An ankle joint performs dorsi flexion and plantar flexion motions, andadduction and abduction motions. FIG. 6 illustrates a direction ofplantar flexion and dorsi flexion, and a range of motion. A direction inwhich a toe is pressed down toward the sole is the plantar flexiondirection, and an opposite direction is the dorsi flexion direction.FIG. 7 illustrates a direction of adduction and abduction and a range ofmotion. A direction in which a toe approaches the median axis is theadduction, and a direction in which a toe moves away from the medianaxis is the abduction.

(4) Time Factors of Gait

In the case of general gait, the heel contacts the ground first, and thetoe leaves the ground last. In particular, an action in which a heelcontacts the ground during gait is called heel contact or heel strike,and an action in which a toe leaves the ground is called toe off. A timerequired from the heel contact to the next heel contact of the same footis called a gait cycle. The gait cycle is divided into a stance phaseand a swing phase. The stance phase indicates a phase from the heelcontact to the toe off, i.e., a state in which the foot is on theground. The swing phase is a phase from the toe off to the heel contact,i.e., a state in which the foot is off the ground. In the case ofhealthy gait, the stance phase and the swing phase of the gait cycleaccount for about 60% and about 40%, respectively.

(5) Methods of Expressing Three-Dimensional Postures

Herein, methods of expressing an “orientation (posture)” of a coordinatesystem in a three-dimensional space are described. Expressions ofdirections in a three-dimensional space include “direction” and“orientation”. They differ, in short, in that the direction is thedirection of a vector and the orientation is the posture of a coordinatesystem. For example, as illustrated in FIG. 8(a), a direction having avector is illustrated. A rotation about the axis of the vector does notprovide any apparent change. As illustrated in FIG. 8(b), an orientationhaving a coordinate system is illustrated. Even when a rotation is madeabout one basic axis therefrom, the rotation can be observed accordingto a change of the direction of another basic axis. When therelationship between the orientations of two coordinate systems can beexpressed by conversion by means of a unit matrix E, the relationshipbetween the two coordinate systems is said to be in an “identicalstate”. In the identical state, the corresponding basic axes of the twocoordinate systems are parallel to each other. An angular displacementfrom the identical state is called the orientation. The angulardisplacement indicates a quantity varying with rotation.

(6) Matrix

In a three-dimensional coordinate system, a general method of expressingthe orientation in the field of mathematics is a matrix. A coordinatesystem O-XYZ and a coordinate system O′-xyz illustrated in FIG. 9 areconsidered in a three-dimensional space. The coordinate system O′-xyzcan freely move in the coordinate system O-XYZ. At this time, theorientation of the coordinate system O′-xyz, which is observed from thecoordinate system O-XYZ, is determined.

The coordinate system O′-xyz starts in the identical state with respectto the coordinate system O-XYZ, and predetermined rotation operation isperformed. The orientation of the coordinate system O′-xyz as of thepresent time is illustrated. Now, when basic vectors e_(x), e_(y), e_(z)of O′-xyz are known to be vectors of the coordinate system O-XYZ, arotation matrix indicated in Equation (1) is determined from these threevectors.

[Equation 1]

R _(XYZ→xyz) =[e _(x) e _(y) e _(z)]  (1)

By making use of the fact that Equation (1) is an orthogonal matrix,inverse conversion is determined by transposition of it.

[Equation 2]

R _(xyz→XYZ) =[e _(x) e _(y) e _(z)]  (2)

(7) Euler Angles

As a general method of expressing the motion of a body, there is aconcept called Euler angles. In the field of orthopedic surgery orbiomechanics, the Euler angles are used with respect to the motion of athree-degree-of-freedom joint, e.g., a shoulder joint or a hip joint.The Euler angles are less used for those modeled as a joint with onlyflexion and extension motions, e.g., a knee joint.

The Euler angles are named after Leonhard Euler, who proved that anyorientation can be expressed by rotation of three different axes. Thereare many definitions of the Euler angles depending on the combination ofan order of rotation. Three parameters expressing the amount of rotationdepend on an order of rotation. For correct expression of theorientation, it is necessary to describe the definitions of the Eulerangles to be used. The z-y-x Euler angles, general Euler angles, areintroduced in conjunction with FIG. 10. First, a coordinate system inthe identical state with the coordinate system O-xyz described in (6)above is considered. First, rotation at an angle φ about the z axis isperformed. This is called a “heading angle”. Next, rotation at an angleθ about the y axis after the rotation is performed. This is called a“pitch angle”. Finally, rotation at an angle φ about the x axis afterthe above rotation is performed. This is called a “bank angle”. Equation(3) indicates a rotation matrix of the z-y-x Euler angles.

$\begin{matrix}\left\lbrack {{Equation}\mspace{14mu} 3} \right\rbrack & \; \\\begin{matrix}{R = {R_{z}R_{y}R_{x}}} \\{= \begin{bmatrix}{{C\; \theta_{z}C\; \theta_{y}} - {S\; \theta_{z}S\; \theta_{x}S\; \theta_{y}}} & {{- S}\; \theta_{z}C\; \theta_{x}} & {{C\; \theta_{z}C\; \theta_{y}} + {S\; \theta_{z}S\; \theta_{x}S\; \theta_{y}}} \\{{S\; \theta_{z}C\; \theta_{y}} + {C\; \theta_{z}S\; \theta_{x}S\; \theta_{y}}} & {C\; \theta_{z}C\; \theta_{x}} & {{S\; \theta_{z}C\; \theta_{y}} - {C\; \theta_{z}S\; \theta_{x}S\; \theta_{y}}} \\{{- C}\; \theta_{z}S\; \theta_{y}} & {S\; \theta_{x}} & {C\; \theta_{x}S\; \theta_{y}}\end{bmatrix}}\end{matrix} & (3)\end{matrix}$

In Equation (3), symbols sin and cos are abbreviated as s and c,respectively. Symbols R_(x), R_(y) and R_(z) are as described inEquations (4) to (6).

$\begin{matrix}\left\lbrack {{Equation}\mspace{14mu} 4} \right\rbrack & \; \\{R_{x} = \begin{bmatrix}1 & 0 & 0 \\0 & {\cos \; \theta_{x}} & {{- \sin}\; \theta_{x}} \\0 & {\sin \; \theta_{x}} & {\cos \; \theta_{x}}\end{bmatrix}} & (4) \\\left\lbrack {{Equation}\mspace{14mu} 5} \right\rbrack & \; \\{R_{y} = \begin{bmatrix}{\cos \; \theta_{y}} & 0 & {\sin \; \theta_{y}} \\0 & 1 & 0 \\{{- \sin}\; \theta_{y}} & 0 & {\cos \; \theta_{y}}\end{bmatrix}} & (5) \\\left\lbrack {{Equation}\mspace{14mu} 6} \right\rbrack & \; \\{R_{z} = \begin{bmatrix}{\cos \; \theta_{z}} & {{- \sin}\; \theta_{z}} & 0 \\{\sin \; \theta_{z}} & {\cos \; \theta_{z}} & 0 \\0 & 0 & 1\end{bmatrix}} & (6)\end{matrix}$

The rotations of the Euler angles in the case of inverse conversion,i.e., when rotation is performed in an order of x-y-z axes, are called aroll angle, a pitch angle, and a yaw angle, respectively. These arecalled Cardan angles, which are most frequently used in biomechanics.

The number of parameters minimally required for expression of athree-dimensional angular displacement is three. The Euler angles areexpressed by minimally required three angles. In addition, suchparameters are directly linked to angle data and are therefore veryintuitive. However, the Euler angles are merely a forward kinematical“orientation expressing method”, but are not a calculation method.Calculation is somewhat troublesome when an orientation indicated bycertain Euler angles is changed to an orientation indicated by differentEuler angles. In addition, there is also a problem called gimbal lock.Also from a viewpoint of algorithm construction, the Euler angles arenot a preferable method because of conditional processing with regard tosingularities and an increase in number of times of calculation asindicated by Equation (3).

(8) Quaternions

The quaternion is a type of “hypercomplex numbers”, which is anextension of complex numbers. In recent years, the quaternion is appliedto the field of 3D computer graphics and spacecraft attitude control.

The quaternion is formed of one scalar element and one vector element.As methods of expressing a quaternion, there are various methodsincluding a method of expressing a quaternion as a matrix and a methodof expressing a quaternion using an exponential map. Herein, theexpression described below is used.

[Equation 7]

Q=W+X _(i) +Y _(j) +Z _(k)=(W; X, Y, Z)=(W;V)   (7)

Symbols W, X, Y and Z are quaternion parameters. Similar to V, symbolsX, Y and Z can be expressed as vectors. When quaternions are used in anorientation expressing method, the quaternions are easier to understandas they are expressed as vectors. Symbols i, j and k are calledquaternion units that are similar in property to imaginary numbers.

[Equation 8]

i ² =j ² =k ² =ijk=−1   (8)

The quaternion has a norm, which is defined in Equation (9).

[Equation 9]

|Q|=√{square root over (W² +X ² +Y ² +Z ²)}  (9)

The quaternion having ∥Q∥=1 is particularly called a unit quaternion,which is indicated by Equation (10).

[Equation 10]

q=Q/∥Q∥=(w; x, y, z)   (10)

The quaternion is a type of hypercomplex numbers. Therefore, similar tocomplex numbers, there is a concept called a conjugate quaternion, whichis indicated by Equation (11).

[Equation 11]

Q*=(W; −V)   (11)

In the case of q=(w₁; v₁) and q₂=(w₂;v₂), a product of the unitquaternions is indicated by Equation (12).

[Equation 12]

q ₁ {circle around (×)}q ₂=(w ₁ ; v ₁) {circle around (×)} (w ₂ ; v₂)=(w ₁ w ₂ −v ₁ v ₂ ; w ₁ v ₂ +w ₂ v ₁ +v ₁ ×v ₂)   (12)

A geometric significance of the quaternion is described. The unitquaternion indicating rotation can be indicated by Equation (13) usingcos and sin.

$\begin{matrix}\left\lbrack {{Equation}\mspace{14mu} 13} \right\rbrack & \; \\{q = \left( {{\cos \; \frac{\theta}{2}};{n\; \sin \; \frac{\theta}{2}}} \right)} & (13)\end{matrix}$

Here, symbol n is a unit vector. Now, a vector r in a three-dimensionalspace is considered. This vector is indicated as r=(0; r_(x), r_(y),r_(z)) in quaternion notation. A real component may be any value andhere is zero for the sake of simplicity.

The rotation in a three-dimensional space can be expressed inconjunction with the description given heretofore. When r defined aboveis rotated to be r′, this phenomenon can be expressed by Equation (14).

[Equation 14]

r′=q{circle around (×)}r{circle around (×)}q*   (14)

In this case, the unit quaternions n and θ used for rotation indicatedin Equation (13) indicate a vector indicating an axis of rotation andthe amount of rotation about the axis, respectively.

According to the present invention, as will be described below, thequaternions are used for computation of angular displacement.

In view of the above, an embodiment of the present invention isdescribed in detail on the basis of the drawings. A gait analysis systemand a gait analysis method according to the embodiment measureacceleration and angular velocity of a body part during gait of asubject, estimates a lower limb posture on the basis of the measurementdata, and calculates a gait parameter required for assessment of gait.

As illustrated in FIG. 11, a gait analysis system 1 includes sensorunits 3 for measuring acceleration and angular velocity of a body partduring gait, a processing device 5 for acquiring acceleration data andangular velocity data from the sensor units 3 and executing processingof calculating a parameter for gait assessment, and a monitor screen 7for displaying results of gait assessment.

(Sensor Units)

Each sensor unit 3 is formed as one tri-axial acceleration sensor, onebi-axial angular velocity sensor, and one uni-axial angular velocitysensor are configured as a unit. The sensor unit 3 detects accelerationof perpendicular three axial directions and angular velocity about theaxes. The acceleration sensor and the angular velocity sensor may not beconfigured as a unit. As the sensor unit 3, for example, WAA-00 6manufactured by Wireless Technologies, Inc. may be used. In the presentembodiment, seven sensor units 3 are used. The attachment locations andthe method will be described later.

Each sensor unit 3 is configured to transmit acceleration data andangular velocity data detected by the acceleration sensor and theangular velocity sensor, respectively, to the processing device 5 inreal time via wireless communication. Each sensor unit 3 includes asoftware timer. At the timing of measurement of acceleration and angularvelocity with the internal sensors, a timer value is stored together.Thus, all the sensor units are synchronized. A sampling frequency is setto 100 Hz.

FIGS. 12(a) and (b) illustrate attachment positions and an attachmentmethod for the sensor units 3 with respect to a subject (testee) at thetime of data measurement. A total of seven sensor units 3 are attachedto the pelvis, the right and left thighs, the right and left shanks, andthe right and left feet, respectively. The sensor units 3 may be fixedin a predetermined position by being housed in pockets formed on sportstights or pockets formed on a sports band worn by a subject during gait.The sensor units 3 are not subjected to any particular limitationregarding fixing position, but may be arranged at any location on theaforementioned portions. However, in order to minimize the angularvelocity that can be generated on the sensors by the muscle activity, itis preferable that the sensor unit 3 on the pelvis be fixed to themidpoint of the right and left posterior iliac crests, the sensor units3 on the thighs be fixed to the quadriceps muscle middle portions, andthe sensor units 3 on the shanks be attached to the inner sides of thefront parts of the tibiae. The sensor units 3 on the feed can be fixedto the surfaces of shoes by means of a sports band or the like. However,it is preferable to avoid the vicinity of the metatarsal joint and toselect proper locations to be free of influences by plantar and dorsiflexion. The directions of the sensor units 3 when fixed may bearbitrary because the directions are corrected by a method that will bedescribed later. Incidentally, reference numeral 4 in the drawingsindicates markers that will be described later.

(Modeling of Lower Limbs)

Next, modeling of lower limbs is described. In the present embodiment, athree-dimensional wire-frame model such as that illustrated in FIG. 13is constructed to express the posture of a body part during gait. Thisis an extension of a method of expressing a part of a body as a rigidbody link model, and a plane is formed of wires. This enables expressionof not only the directions, but also the posture (orientation) of a bodypart. Parts expressed by wires are regarded as rigid bodies, which arecalled segments for the sake of convenience. Each of the segments iscapable of independent motion. The lower limb model is formed of a totalof seven segments: a pelvis segment, right and left thigh segments,right and left shank segments, and right and left foot segments. Thedetails are described below.

The pelvis segment is formed of six points: right and left anteriorsuperior iliac spines, right and left posterior iliac crests, and rightand left hip joint centers.

The thigh segment is formed of four points: a hip joint center, a greattrochanter, a medial knee joint space, and a lateral knee joint space.

The shank segment is formed of a lateral condyle of tibia, a medial kneejoint space, a lateral knee joint space, and an ankle joint center. Theankle joint center is a midpoint of the lateral malleolus and the medialmalleolus.

The ankle joint segment is formed of three points: an ankle jointcenter, a heel bone, and a toe.

(Measurement of Body Dimensions)

The construction of a wire-frame model requires body dimensions. Thebody dimensions measured at the time of gait measurement are describedbelow. In this system, the body dimensions may be input with an inputmeans, e.g., a keyboard connected to the processing device.

-   -   Intertrochanteric distance: A straight-line distance between        right and left great trochanters    -   Thigh length: A distance from a great trochanter to a lateral        epicondyle of femur    -   Shank length: A distance from a lateral condyle of tibia to an        ankle joint lateral malleolus

The pelvis segment is modeled such that the pelvis segment has anaverage shape consistently and the size varies in proportion to theintertrochanteric distance.

(Definition of Coordinate Systems)

In the present embodiment, for calculation and expression of gaitpostures, three types of coordinate systems: a sensor coordinate system,a ground coordinate system, and a segment coordinate system are used. Aright thigh is taken as an example, and three coordinate systems areillustrated in FIGS. 14(a) and (b). In these drawings only, the sensorcoordinate system is indicated by reference symbol C_(sn), the groundcoordinate system is indicated by reference symbol C_(e), and thesegment coordinate system is indicated by reference symbol C_(sg).

The ground coordinate system is a stationary system for observation ofmotion, and is defined such that the z-axis is taken vertically upwardand the x-axis is taken parallel to the initial sagittal-horizontal axisof a subject and anteriorly from the subject. The y-axis is taken to beperpendicular to both of them to form a right-handed system.

FIGS. 15(a) and (b) illustrate the definition of the coordinate systemof the thigh segment. The z-axis is taken parallel to a line connectingthe great trochanter and the lateral knee joint space, and thesagittal-horizontal axis (front direction, walking direction) is takenas the x-axis.

FIGS. 16(a) and (b) illustrate the definition of the coordinate systemof the shank segment. The z-axis is taken parallel to a line connectingthe knee joint center and the ankle joint center, and thesagittal-horizontal axis (front direction, walking direction) is takenas the x-axis. The knee joint center is a midpoint of the lateral kneejoint space and the medial knee joint space, and the ankle joint centeris a midpoint of the ankle joint lateral malleolus and the ankle jointmedial malleolus.

The coordinate systems of the pelvis segment and the foot segments aredefined to correspond to the ground coordinate system in a standingposture. When the standing posture is assumed, the toes are directedforward and the feet are aligned.

(Processing Device)

Next, returning to FIG. 11, the processing device 5 of the gait analysissystem is described. Additionally, a processing flow with the system isillustrated in FIG. 17. In the present embodiment, the processing device5 uses a personal computer, but may be anything insofar as it canacquire acceleration data and angular velocity data from the sensorunits 3 and perform predetermined computation processing to indicate apredetermined gait parameter on the monitor screen 7 or output or recorda predetermined gait parameter on a different device.

As illustrated in FIG. 11, the processing device 5 includes a dataacquisition portion 11 for acquiring acceleration data and angularvelocity data from each sensor unit 3, a sensor posture estimationportion 13 for estimating the posture (orientation) of the sensorcoordinate system on the basis of the acceleration data and the angularvelocity data of each body part, the acceleration data and the angularvelocity data being acquired by the data acquisition portion 11, asegment posture computation portion 15 for computing the posture of eachsegment by converting the posture estimated by the sensor postureestimation portion 13 into the posture (orientation) of the segmentcoordinate system, a lower limb posture computation portion 17 forcreating each segment on the basis of the posture of each segmentcomputed by the segment posture computation portion 15 and bodydimensions input and coupling the created segments in a predeterminedposture so as to compute a lower limb posture (three-dimensionalwire-frame model) during gait, and a gait parameter computation portion19 for calculating a gait parameter on the basis of the lower limbposture computed by the lower limb posture computation portion 17. Thedata acquisition portion 11, the sensor posture estimation portion 13,the segment posture computation portion 15, and the lower limb posturecomputation portion 17 described above constitute the model constructionmeans of the present invention. In addition, the aforementioned gaitparameter computation portion 19 constitutes the gait parametercalculation means of the present invention.

The sensor posture estimation portion 13 estimates the posture of thesensor during gait in the manner described below.

First, in the case of plane rotation, an angular displacement θ can becalculated by Equation (15).

[Equation 15]

θ=θ₀+∫₀ ^(t) ωdt   (15)

In Equation (15), the first term of the right-hand side indicates aninitial posture (orientation), and the second term indicates an angulardisplacement from the initial posture. In the present embodiment, theinitial posture is estimated through the use of the acceleration dataobtained by the acceleration sensor. Furthermore, the angulardisplacement is estimated through the use of the angular velocity dataobtained from the angular velocity sensor.

The principle of determining the initial posture of the sensor from theacceleration data is described with reference to FIG. 18. Theacceleration sensor detects a motion acceleration a and a gravitationalacceleration g simultaneously.

Equation 16]

S=a−g   (16)

In particular, for example, at rest or in constant velocity motion, whenmotion acceleration does not apply with respect to the accelerationsensor, the acceleration sensor detects a gravitational accelerationcomponent only.

[Equation 17]

S=−g   (17)

Accordingly, an angle formed by the vertical axis (gravity direction)and the detection axes of the acceleration sensor can be calculated fromthe proportion of the detection axes of the acceleration sensor and thevector sum.

$\begin{matrix}\left\lbrack {{Equation}\mspace{14mu} 18} \right\rbrack & \; \\{\theta = {\sin^{- 1}\frac{g_{x}}{g}}} & (18)\end{matrix}$

In the case of three dimensions, in principle, even when rotation occursabout the gravity axis, it is impossible for the acceleration sensor todetect the acceleration, and only the initial posture is detected by theacceleration sensor. Therefore, the heading angle of the aforementionedEuler angles at a time when a subject assumes the initial posture may bedefined to be 0°.

Next, the angular displacement is determined. Parameters input to unitquaternions indicating rotation include the axis of rotation and theamount of rotation about the axis. The quaternion is used to calculatethe angular displacement because it is easy to match up with the angularvelocity data obtained by the angular velocity sensor. An axis ofrotation n and an amount of rotation θ are indicated by Equations (19)and (20) described below, respectively.

$\begin{matrix}\left\lbrack {{Equation}\mspace{14mu} 19} \right\rbrack & \; \\{n = \frac{\omega}{\omega }} & (19) \\\left\lbrack {{Equation}\mspace{14mu} 20} \right\rbrack & \; \\{\theta = {{\omega }\Delta \; t_{s}}} & (20)\end{matrix}$

Symbol ω indicates an angular velocity vector obtained from the detectedacceleration of each axis of the angular sensor, and symbol Δt_(s)indicates a sampling period. They are substituted into theaforementioned Equation (13), and the result is described below.

$\begin{matrix}\left\lbrack {{Equation}\mspace{14mu} 21} \right\rbrack & \; \\{q = \left( {{\cos \; \frac{{\omega }\Delta \; t_{s}}{2}};{\frac{\omega}{\omega }\sin \frac{{\omega }\Delta \; t_{s}}{2}}} \right)} & (21)\end{matrix}$

As a result of the input, a micro angular displacement per samplingperiod in which the angular velocity vector is the axis of rotation isobtained. Then, as this is integrated in time domain, the angulardisplacement from the initial posture is determined. In this way, thesensor posture estimation portion 13 estimates the posture of the sensorunits 3.

Next, conversion of coordinate systems by the segment posturecomputation portion 15 is described. According to the present invention,the sensor units 3 are attached to body parts corresponding to therespective segments and measurement is performed to determine theposture of each body part (segment). However, it is difficult orimpossible to attach the sensor units 3 such that the sensor coordinatesystem corresponds to the segment coordinate system. Therefore, forestimation of the motion of the segments, it is necessary that anexperiment different from the gait experiment be performed to determinethe relative postures between the sensor coordinate system and thesegment coordinate system, and the posture of the sensor coordinatesystem be converted into the posture of the segment coordinate system.

Under conditions that factors including muscle contraction, clothing,and skin displacement are negligible, the sensor unit 3 and the segmentexhibit a similar angular motion. Therefore, when the posture of thesensor unit 3 is determined, the posture of the segment can bedetermined as a result of rotation operation.

In reality, the following two processes are taken to determine therotation matrix from the sensor coordinate system to the segmentcoordinate system.

-   -   Rotation matrix from the sensor coordinate system to the ground        coordinate system    -   Rotation matrix from the ground coordinate system to the segment        coordinate system

The manner of determining the rotation matrix from the sensor coordinatesystem to the ground coordinate system is described. The accelerationdata is measured when a subject is at rest in a standing posture or atrest in a seated posture. The standing posture is a state that a subjectupstands on a horizontal ground where both toes are aligned asillustrated in FIG. 16. The seated posture is as illustrated in FIG. 19.The toes are also aligned in the seated posture. Thus, the gravitationalaccelerations in the case of the two postures: the standing posture andthe seated posture can be obtained.

The manner of determining the rotation matrix from the sensor coordinatesystem to the ground coordinate system on the basis of the above isdescribed in conjunction with FIG. 20. An arrow g positioned at themiddle indicates the gravitational acceleration in the standingposition, and an arrow g positioned on the right side indicates thegravitational acceleration in the seated position. The z-axis of theground coordinate system is defined to be the direction opposite to thatof the gravitational acceleration in the standing position. The y-axisis defined by a cross product of the gravitational acceleration in thestanding position and the gravitational acceleration in the seatedposition. The x-axis is defined by a cross product of the y-axis and thez-axis.

Thus, the basic vector of the ground coordinate system with respect tothe sensor coordinate system can be acquired.

The rotation from the ground coordinate system to the segment coordinatesystem provides the segment coordinate system with respect to the groundcoordinate system from a front view photograph and a side viewphotograph in the standing posture as illustrated in FIG. 14, and therotation matrix from the ground coordinate system to the segmentcoordinate system can be obtained.

In addition, the system of the present embodiment includes a filteringmeans. The data obtained by the angular velocity sensor includes noise.Because the noise is high frequency, the noise can be removed by alow-pass filter. As the low-pass filter, for example, a Butterworthfilter of an IIR digital filter may be used. In this case, the cutofffrequency can be 12 Hz. However, the use of this filter results ingeneration of a phase delay, but the filtering processing with the sameproperty is performed twice in total: one before the data and the otherafter the data to eliminate the phase delay. FIG. 21 illustrates resultsof the low-pass filter processing by comparing the states before andafter the filtering processing.

In addition, the data obtained from the angular velocity sensor containbias. This is described in conjunction with an angular velocity waveformat the time of gait measurement illustrated in FIG. 22. The horizontalaxis indicates the time elapsed from beginning of measurement, and thevertical axis indicates the angular velocity about the y-axis of thesensor arranged on the right thigh. The angular velocity sensor recordsa non-zero value as a detected value even at rest. This is a bias of theangular velocity. As described above, in the present embodiment, themethod of calculating the angular displacement includes an integrationelement. Therefore, biases are accumulated during numerical integration,which directly leads to errors. Thus, it is necessary that the amount ofbias be estimated and be subtracted from the original data beforeintegration calculation. There are various bias estimation methods.Here, for bias estimation, the mode of raw data is estimated to be bias.

The gait parameter computation portion 19 calculates various types ofparameters required for gait assessment from the lower limb posturecomputed by the lower limb posture computation portion with apredetermined program and the timings of the heel contact and the toeoff. The timings of the heel contact and the toe off can easily bedetermined by means of an optical system or a floor reaction forcegauge. However, in the present embodiment, only the acceleration andangular velocity data are used for detection. Specifically, as describedbelow, the timing of the heel contact is detected from the angularvelocity data of the shank, and the timing of the toe off is detectedfrom the relative positions of the right and left toes.

As illustrated in FIG. 23, the angular velocity of the shank during gaitis close to 0 degrees/second in the stance phase, and a relatively largeangular velocity is generated in the swing phase because the shank isswung forward. Immediately before the heel contact, the shank swungforward is slightly pulled backward. Therefore, the peak value of theangular velocity appears in the direction opposite to that of the swingphase. This peak position is used for detection of the heel contact.

FIG. 24 illustrates a distance in walking direction from the originalpoint (midpoint of the right and left hip joint centers) to the righttoe. This is a graph indicating a standing state at rest at the onsetand the beginning of gait at the point near 1.5 seconds. When the gaitbegins, first, the right leg is swung forward, and the distance from theoriginal point increases in a positive direction. The heel contact ismade slightly after the positive peak position. Upon entry into thestance phase, the distance from the original point decreases, andsubsequently the toe is shifted backward beyond the original point.Therefore, the distance from the original point increases in a negativedirection. Then, the toe off is made, and the right leg again begins toswing forward, and the distance from the original point startsincreasing in the positive direction. Until the toe off is made, thedistance from the original point monotonically increases in the negativedirection. Therefore, the negative peak position presumably correspondsto the timing of the toe off. In the present embodiment, the relativeposition of the toe is calculated from the lower limb posture obtainedby the lower limb posture computation portion 17, and the timing atwhich the relative distance from the original point assumes the negativepeak position is the timing of the toe off.

Next, gait parameters calculated by the gait parameter computationportion 19 from the lower limb posture computed by the lower limbposture computation portion 17 and the timings of the heel contact andthe toe off are described below. These gait parameters are commonly usedfor diagnosis of a patient with knee osteoarthritis (knee OA), forexample, in gait analysis through observation by a doctor or a physicaltherapist.

(a) Step Length: Step Length

The distance between the heel in heel contact and the heel of theopposite leg

(b) Maximum Knee Flexion Angle: Max Knee Flexion in Swing

The maximum value of a knee flexion angle observed in the swing phase

(c) Maximum Knee Extension Angle: Max Knee Extension in Stance

The maximum value of a knee extension angle observed in the stance phase(minimum value of knee flexion angle)

(d) Range of Motion of Knee Joint:ROM of Knee

The value obtained as the maximum knee extension angle is subtractedfrom the maximum knee flexion angle

(e) Knee Flexion Angle (Immediately After Heel Contact): Max KneeFlexion in Stance

The knee flexion angle at the time of an increase in the flexion angleobserved immediately after the heel contact

(f) Knee Flexion Angle (At the Time of Toe Off):Knee Flexion at Toe Off

The knee flexion angle at the time of the toe off

(g) Ankle Abduction Angle: Ankle Abduction in Stance

The direction of the toe with respect to the walking direction in stance

(h) Thigh and Shank Angle: FTA in Stance

The maximum value of an angle formed by the z-axis of the thigh and thez-axis of the shank in the coronal plane in the stance phase

(i) Lower Limb Functional Axis Inclination Angle (Abduction Direction):Maximum Inclination of Functional Axis of Lower Extremity in Stance

The maximum value of an angle formed by a line connecting the hip jointcenter and the ankle joint center and the vertical axis in the sagittalplane in the stance phase (maximum abduction)

(j) Lower Limb Functional Axis Inclination Angle (Adduction Direction):Minimum Inclination of Functional Axis of Lower Extremity in Stance

The minimum value of an angle formed by a line connecting the hip jointcenter and the ankle joint center and the vertical axis in the sagittalplane in the stance phase (maximum adduction)

(k) Gait Cycle:Gait Cycle

The time from the heel contact to the toe off and to the next heelcontact

(l) Stance Ratio: Stance Phase

The quotient obtained by dividing the time (stance time) from the heelcontact to the toe off by the gait cycle

In addition to the aforementioned gait parameters, the gait parametercomputation portion 19 calculates two further novel gait parameters. Thenovel assessment parameters can be obtained through the use of aLissajous figure. The Lissajous figure is a “plane figure obtained on anorthogonal coordinate as two simple harmonic motions are combined”. Inthe field of gait measurement, the Lissajous figure indicates a motiontrajectory of a joint or a gravity center position in the sagittalplane, the horizontal plane, or the coronal plane. Regarding theLissajous figure, currently, only the motion trajectory in the coronalplane is used, for example, in the field of gait research. This isbecause gait is a motion involving movement, and therefore in the caseof an optical system or the like, a motion trajectory in the sagittalplane or the horizontal plane does not draw a closed curve, but forms asingle wave-like trajectory, which renders it difficult to handle.Meanwhile, with the gait analysis system including the property in whicha lower limb posture is calculated as the midpoint of the right and lefthip joint centers is used as the original point, and the Lissajousfigure of each joint can be obtained as a closed curve in all the planes: the sagittal plane, the horizontal plane, and the coronal plane. Inthe present embodiment, the Lissajous figure is drawn by the gaitparameter calculation portion 19.

The first novel gait parameter is a knee acceleration vector direction.FIG. 25 illustrates motion trajectories of joints (great trochanter,knee joint, ankle joint) in the sagittal plane. The original point isthe midpoint of the right and left hip joint centers, and the rightwarddirection in the plane of paper is the walking direction. The arrow linesupplementary indicated on the motion trajectory of the knee jointindicates the acceleration vector at the time of the heel contact. Theparameter calculation portion 19 calculates an angle θ_(acc) of theacceleration vector with regard to the knee joint trajectory as anassessment parameter.

The other novel gait parameter is a trajectory angle in a knee jointhorizontal plane. FIG. 26 illustrates motion trajectories of knee jointsin the horizontal plane. The original point is the midpoint of the rightand left hip joint centers, and the upward direction in the plane ofpaper is the walking direction. The left closed curve is the motiontrajectory of the left knee joint, and the right closed curve is themotion trajectory of the right knee joint. In the drawing, straightlines extending substantially up and down in the motion trajectories areobtained as the motion trajectories are approximated to a straight line.The parameter calculation portion calculates an angle θ_(xy) formed bythe two straight lines as an assessment parameter.

FIG. 27 illustrates a method of data processing using the gait analysissystem configured in the aforementioned manner. First, raw data obtainedin a gait experiment passes through a low-pass filter and a high-passfilter. Next, the initial posture and the angular displacement of eachsegment are calculated through the calculation of the posture of thesensor unit 3 during gait and the conversion of coordinate systems fromthe sensor coordinate system to the segment coordinate system. Thecalculation uses quaternions, and therefore in this stage the initialposture and the angular displacement are expressed in terms ofquaternions. As described above, the mode is used to estimate an angularvelocity bias. Therefore, the bias estimation precision depends onresolution. Accordingly, the angular displacement, a result of itsintegration, includes integration drift of estimation errors. Becausedrift cannot be removed by a high-pass filter while the quaternions areleft as they are. Therefore, first, the quaternions are converted toEuler angles and the integration drift is removed with respect to theresultant three Euler angles. Thus, when the posture of each segment isdetermined, next, each segment is created on the basis of bodydimensions and the segments are coupled together to construct the lowerlimb posture during gait. The aforementioned various types of gaitparameters can be calculated on the basis of the lower limb posture.

Next, an experiment conducted to confirm the effect of the gait analysismethod and the gait analysis system according to the present inventionis described. The present invention is not limited to the scope of theexperiment described below.

(Experimental Procedure)

First, a procedure of an experiment conducted is briefly illustrated inFIG. 28. First, the seven sensor units 3 were attached to parts, and tenmarkers 4 (see FIG. 12) were attached to the right and left greattrochanters, the medial and lateral knee joint spaces, ankle jointmedial malleolus and lateral malleolus, respectively. Next, bodydimensions (intertrochanteric distance, thigh length, shank length) weremeasured. Next, acceleration data for use in conversion of coordinatesystems from the sensor coordinate system to the segment coordinatesystem was measured. In this case, the standing posture of a subject wasphotographed from the front side, the left side, and the right side.Then, gait was measured (measurement of acceleration and angularvelocity). Conditions of gait will be described later. The various typesof gait parameters, the graphs, and the motion trajectories describedabove were obtained through analysis using a program on the basis of theacceleration and angular velocity data obtained by the measurement up tothis point, and the photographs.

(Reproducibility Study Experiment)

On the assumption of operation at clinical site, measurement using thegait analysis method and the gait analysis system according to thepresent embodiment has to be reproducible. As used herein, thereproducibility of measurement indicates the following two meanings:reproducibility at a time when different measurers measure the samesubject, and reproducibility at a time when the same subject is measuredon different days (day-to-day reproducibility). Specifically, it isrequired that measurement can be done by any measurer and follow-upafter treatment of a subject can be understood correctly.

The subjects included eight healthy males without lower limb history.The averages and the standard deviations of age, weight, height, BMI,and body dimensions are indicated in Table 1 together with values of aknee OA patient group to be described later.

TABLE 1 Healthy group Knee OA group Average Average (Standard (Standarddeviation) deviation) Age [years] 22.9 (0.8) 68.7 (4.1) Weight [kg] 69.1(5.4) 54.2 (5.9) Height [m] 1.74 (0.05) 1.52 (0.05) BMI [kg/m²] 23.0(1.6) 23.5 (2.5) Thigh length [cm] 38.0 (2.3) 32.4 (2.7) Shank length[cm] 40.8 (1.6) 35.6 (1.7) Distance between the greater 35.6 (1.5) 34.5(1.5) trochanters [cm]

Next, experimental conditions are described. Two types of gaitexperiments were conducted: on a straight flat way of 7 m and on atreadmill (Gait Trainer 2™ manufactured by BIODEX Inc.) illustrated inFIGS. 29(a) and (b), respectively.

The gait measurement on the straight flat way started from a standingresting state illustrated in FIG. 16. The subjects walked at givenvelocity and then again assumed a standing resting state.

The gait measurement on the treadmill started from a standing restingstate on the belt at rest. The belt velocity was gradually increased to3 km per hour, and after gait at a steady velocity, the belt was againstopped, and the subjects assumed a standing state. The duration fromthe start to the end was consistently about 20 seconds.

In order to study a difference between measurement results depending onthe measurer, two measurers (indicated as Measurers A_(1st) and B_(1st))separately conducted the same experiment on the same day to performmeasurement on each subject. In addition, in order to study a differencebetween measurement results depending on the measurement date, MeasurerA performed the same trial on each subject about one week after thefirst measurement to again conduct measurement (indicated as MeasurerA_(2nd)). The measurement was performed once with respect to each gaitcondition and measurement condition, and a total of six measurementresults were obtained per person.

For calculation of the gait parameters, which were measurement results,data excluding the beginning and the end of the gait was used. In thecase of level ground gait, data including a total of four steps: tworight steps and two left steps was used, and in the case of treadmillgait, data including a total of ten steps: five right steps and fiveleft steps was used.

(Gait Measurement Experiment on Knee OA Patients)

The subjects of a gait measurement experiment on knee OA patientsinclude ten medial knee OA patients. The averages and the standarddeviations of age, weight, height, BMI, and body dimensions areindicated in Table 1 described above, and information regarding symptomsis indicated in Table 2. In Table 2, Patient B is male and the otherpatients are female. In the Table, symbol “-” indicates that nodiagnosis has been conducted, not indicating absence of symptoms.

TABLE 2 Severity of Pain during Kellgren-Lawrence grade Patientcondition gait Right knee Left knee A R < L Mild Moderate Severe B R < LNone Moderate Moderate C R = L None Suspicious Moderate D R < L None —Moderate E R = L Mild — Moderate F R < L Mild — Mild G R > L NoneModerate — H R = L None — Moderate I R > L Mild — Moderate J R > L MildModerate —

The gait measurement experiment on the knee OA patients was conducted inthe same manner as the reproducibility study experiment. However,because gait on a treadmill requires getting used to and from a safetyperspective, the walkway included a straight flat way of 7 m only. Themeasurement was conducted once by Measurer A on each subject. Forcalculation of the gait parameters, which were measurement results, dataincluding a total of six steps: three right steps and three left stepsexcluding the beginning and the end of the gait was used.

(Results of Reproducibility Study)

Results of the reproducibility study experiment are indicated in Tables3 to 6. The Tables respectively indicate results of a comparison betweenmeasurement dates in the case of level ground gait, results of acomparison between measurers in the case of level ground gait, resultsof a comparison between measurement dates in the case of treadmill gait,and results of a comparison between measurers in the case of treadmillgait. The parameters of the eight healthy persons under each condition,and the average values and the standard deviations of absolutedifferences between the conditions are described in the Tables. Inaddition, a paired t-test was conducted as a significance test betweenthe results of the conditions. It was a two-tailed test with asignificance level of 5%. The p values at this time are described in theTables. The gait of the healthy persons did not exhibit a difference inparameter between the right and left legs. Therefore, the average valuesand the standard deviations in the Tables are calculated on the basis ofthe average values of the right and the left of each subject.

TABLE 3 Measurer Absolute A_(1st) A_(2nd) difference Average AverageAverage (Standard (Standard (Standard deviation) deviation) deviation)p-value Step length [cm] 57.8 (5.0) 58.5 (4.6) 3.8 (2.0) 0.580 Max kneeflexion angle 87.8 (5.0) 85.6 (6.4) 5.6 (4.6) 0.240 in swing [°] Maxknee extension angle 14.7 (6.4) 14.2 (6.9) 3.5 (2.3) 0.675 in stance [°]Range of motion of knee 72.6 (8.1) 70.8 (6.6) 4.1 (3.3) 0.165 joint [°]Knee flexion angle 29.3 (9.8) 28.6 (8.2) 3.8 (3.4) 0.598 (immediatelyafter heel contact) [°] Knee flexion angle (at 61.7 (5.6) 61.9 (6.5) 5.3(3.7) 0.911 the time of toe off) [°] Ankle abduction angle [°] 7.4 (7.9)6.6 (9.5) 2.8 (2.5) 0.391 Thigh and shank angle [°] 184.6 (5.6) 185.3(9.4) 3.7 (2.8) 0.590 Lower limb functional −1.7 (2.4) −2.4 (2.9) 1.9(1.2) 0.197 axis inclination angle (abduction direction) [°] Lower limbfunctional −7.9 (1.7) −7.8 (1.2) 1.3 (0.9) 0.807 axis inclination angle(adduction direction) [°] Gait cycle [s] 1.19 (0.07) 1.19 (0.08) 0.05(0.02) 0.816 Stance ratio [%] 55.5 (2.0) 55.3 (1.9) 0.9 (0.7) 0.521Angle between right 4.7 (7.6) 6.4 (7.4) 4.2 (3.6) 0.416 and left kneejoint tranjectory [°] Direction of knee 62.3 (11.3) 63.2 (7.4) 5.3 (2.0)0.681 acceleration vector (at heel contact) [°]

TABLE 4 Measurer Absolute A_(1st) B_(1st) difference Average AverageAverage (Standard (Standard (Standard deviation) deviation) deviation)p-value Step length [cm] 57.8 (5.0) 60.0 (4.8) 3.2 (2.4) 0.071 Max kneeflexion angle 87.8 (5.0) 82.7 (4.7) 6.2 (4.0) 0.002 in swing [°] Maxknee extension angle 14.7 (6.4) 12.1 (4.7) 3.7 (3.1) 0.027 in stance [°]Range of motion of knee 72.6 (8.1) 70.1 (5.0) 5.1 (3.1) 0.098 joint [°]Knee flexion angle 29.3 (9.8) 25.8 (6.4) 5.6 (4.8) 0.056 (immediatelyafter heel contact) [°] Knee flexion angle (at 61.7 (5.6) 58.5 (5.2) 4.3(2.8) 0.008 the time of toe off) [°] Ankle abduction angle [°] 7.4 (7.9)6.8 (6.3) 3.4 (2.7) 0.578 Thigh and shank angle [°] 184.6 (5.6) 182.7(6.2) 2.5 (1.9) 0.077 Lower limb functional −1.7 (2.4) −2.1 (2.3) 1.0(1.1) 0.348 axis inclination angle (abduction direction) [°] Lower limbfunctional −7.9 (1.7) −7.6 (1.4) 1.2 (1.2) 0.440 axis inclination angle(adduction direction) [°] Gait cycle [s] 1.19 (0.07) 1.21 (0.09) 0.05(0.04) 0.167 Stance ratio [%] 55.5 (2.0) 56.1 (2.1) 1.1 (1.1) 0.107Angle between right 4.7 (7.6) 1.8 (2.1) 5.8 (4.3) 0.288 and left kneejoint tranjectory [°] Direction of knee 62.3 (11.3) 62.5 (10.5) 5.3(3.4) 0.937 acceleration vector (at heel contact) [°]

TABLE 5 Measurer Absolute A_(1st) A_(2nd) difference Average AverageAverage (Standard (Standard (Standard deviation) deviation) deviation)p-value Step length [cm] 44.6 (5.9) 44.7 (5.4) 2.8 (1.8) 0.970 Max kneeflexion angle 80.6 (10.4) 81.4 (7.1) 7.9 (8.0) 0.767 in swing [°] Maxknee extension angle 11.6 (6.8) 12.7 (4.9) 3.0 (3.2) 0.360 in stance [°]Range of motion of knee 68.3 (9.5) 68.1 (8.5) 6.6 (6.8) 0.943 joint [°]Knee flexion angle 26.6 (8.5) 25.5 (7.1) 5.8 (4.7) 0.596 (immediatelyafter heel contact) [°] Knee flexion angle (at 57.1 (9.0) 58.7 (10.6)7.9 (7.5) 0.563 the time of toe off) [°] Ankle abduction angle [°] 7.7(9.5) 6.7 (10.1) 2.2 (1.6) 0.159 Thigh and shank angle [°] 185.5 (7.5)184.6 (6.7) 4.5 (3.6) 0.570 Lower limb functional −3.9 (1.8) −3.0 (2.7)1.3 (1.9) 0.127 axis inclination angle (abduction direction) [°] Lowerlimb functional −8.2 (1.4) −7.8 (1.1) 1.2 (1.0) 0.329 axis inclinationangle (adduction direction) [°] Gait cycle [s] 1.28 (0.11) 1.33 (0.09)0.07 (0.04) 0.016 Stance ratio [%] 56.4 (3.5) 56.5 (2.3) 1.9 (1.8) 0.967Angle between right 1.4 (4.7) 3.0 (5.3) 6.0 (3.3) 0.543 and left kneejoint tranjectory [°] Direction of knee 64.7 (14.8) 79.3 (16.3) 17.8(11.4) 0.040 acceleration vector (at heel contact) [°]

TABLE 6 Measurer Absolute A_(1st) B_(1st) difference Average AverageAverage (Standard (Standard (Standard deviation) deviation) deviation)p-value Step length [cm] 44.6 (5.9) 45.8 (4.8) 3.2 (2.9) 0.316 Max kneeflexion angle 80.6 (10.4) 81.1 (7.7) 5.8 (5.4) 0.789 in swing [°] Maxknee extension angle 11.6 (6.8) 10.9 (5.6) 4.3 (4.7) 0.636 in stance [°]Range of motion of knee 68.3 (9.5) 69.1 (10.0) 5.2 (3.5) 0.594 joint [°]Knee flexion angle 26.6 (8.5) 24.5 (8.0) 5.1 (4.5) 0.231 (immediatelyafter heel contact) [°] Knee flexion angle (at 57.1 (9.0) 56.7 (8.8) 7.3(5.7) 0.895 the time of toe off) [°] Ankle abduction angle [°] 7.7 (9.5)7.8 (8.9) 2.9 (2.2) 0.945 Thigh and shank angle [°] 185.5 (7.5) 185.0(8.4) 4.7 (4.3) 0.769 Lower limb functional −3.9 (1.8) −3.3 (2.1) 1.6(1.3) 0.225 axis inclination angle (abduction direction) [°] Lower limbfunctional −8.2 (1.4) −7.9 (1.5) 1.1 (0.7) 0.412 axis inclination angle(adduction direction) [°] Gait cycle [s] 1.28 (0.11) 1.31 (0.13) 0.05(0.05) 0.079 Stance ratio [%] 56.4 (3.5) 56.1 (2.6) 1.9 (1.4) 0.566Angle between right 1.4 (4.7) 3.9 (4.7) 3.7 (2.9) 0.147 and left kneejoint tranjectory [°] Direction of knee 64.7 (14.8) 71.1 (13.4) 12.2(6.6) 0.215 acceleration vector (at heel contact) [°]

(Results of Gait Measurements on Knee OA Patients)

The measurement results obtained by the gait measurements on the knee OApatients are indicated in Tables 7 to 16 and FIGS. 30 to 39. The Tablesdescribe the parameters of three steps of each of the right leg and theleft leg and their average values and standard deviations. Kneehorizontal plane trajectory angles are calculated not for each gaitcycle, but from the Lissajous figures of gait cycles, and therefore notdescribed in the Tables. FIG. 30(a) is a graph of knee flexion angle.The vertical axis indicates the knee flexion angle, and the horizontalaxis indicates the gait cycle. Gait cycles 0% and 100% are the timing ofthe heel contact. In addition to the right knee flexion angle and theleft knee flexion angle, the Tables describe, in the light-colored linesand region, the average values of the healthy persons measured byMeasurer A_(1st) and its 95% confidence interval. The graphs are theaverage value of three gait cycles. FIGS. 30(b) and (c) illustrate thesagittal plane trajectory of the three gait cycles and the accelerationvector of the second step out of the three steps at the time of the heelcontact. FIG. 30(d) indicates the knee joint horizontal planetrajectories of the three gait cycles. A knee horizontal planetrajectory angle θ_(xy) is described in the upper part of the drawing.Subsequently, similar drawings are illustrated regarding each patient upto FIG. 39. For reference, the sagittal plane trajectories and the kneehorizontal plane trajectories of two gait cycles of the eight healthypersons are illustrated in FIGS. 40 and 41.

TABLE 7 Number of steps Standard 1st step 2nd step 3rd step Averagedeviation Right Step length [cm] 38.9 34.0 39.8 37.6 3.2 leg Max kneeflexion angle in swing [°] 76.3 79.2 79.8 78.5 1.9 Max knee extensionangle in stance [°] 7.8 8.6 8.4 8.3 0.4 Range of motion of knee joint[°] 68.5 70.6 71.4 70.2 1.5 Knee flexion angle (immediately after 14.115.2 15.5 14.9 0.7 heel contact) [°] Knee flexion angle (at the time oftoe 51.7 54.3 58.1 54.7 3.2 off) [°] Ankle abduction angle [°] −0.9 1.24.0 1.4 2.5 Thigh and shank angle [°] 175.5 176.7 174.5 175.6 1.1 Lowerlimb functional axis inclination −2.1 −2.3 −2.0 −2.1 0.2 angle(abduction direction) [°] Lower limb functional axis inclination −5.0−5.4 −4.3 −4.9 0.6 angle (adduction direction) [°] Gait cycle [s] 1.111.13 1.16 1.13 0.02 Stance ratio [%] 59.0 59.8 56.7 58.5 1.6 Directionof knee acceleration vector 32.8 34.9 35.7 34.5 1.2 (at heel contact)[°] Left Step length [cm] 46.1 49.3 47.6 47.7 1.6 leg Max knee flexionangle in swing [°] 70.9 72.4 73.9 72.4 2.6 Max knee extension angle instance [°] 7.5 7.7 8.9 8.0 0.7 Range of motion of knee joint [°] 63.464.8 67.0 65.1 1.8 Knee flexion angle (immediately after 10.8 12.7 13.512.4 1.4 heel contact) [°] Knee flexion angle (at the time of toe 51.652.8 50.2 51.5 1.3 off) [°] Ankle abduction angle [°] −0.7 −2.9 −1.3−1.6 1.2 Thigh and shank angle [°] 176.7 177.8 178.3 177.6 0.8 Lowerlimb functional axis inclination −0.4 −0.9 −2.3 −1.2 1.0 angle(abduction direction) [°] Lower limb functional axis inclination −5.4−5.7 −5.4 −5.5 0.2 angle (adduction direction) [°] Gait cycle [s] 1.121.10 1.18 1.13 0.04 Stance ratio [%] 54.5 54.5 55.7 54.9 0.7 Directionof knee acceleration vector 72.4 64.0 83.1 73.2 7.8 (at heel contact)[°]

TABLE 8 Number of steps Standard 1st step 2nd step 3rd step Averagedeviation Right Step length [cm] 63.4 60.7 62.5 62.2 1.9 leg Max kneeflexion angle in swing [°] 81.7 81.6 81.7 81.7 0.1 Max knee extensionangle in stance [°] 10.1 15.8 12.0 12.6 4.0 Range of motion of kneejoint [°] 71.7 65.8 69.7 69.1 4.1 Knee flexion angle (immediately afterheel 35.9 40.6 37.5 38.0 3.4 contact) [°] Knee flexion angle (at thetime of toe off) 57.4 59.9 58.2 58.5 1.8 [°] Ankle abduction angle [°]11.2 11.0 11.1 11.1 0.1 Thigh and shank angle [°] 187.1 187.8 187.3187.4 0.5 Lower limb functional axis inclination angle 0.5 0.9 0.6 0.70.3 (abduction direction) [°] Lower limb functional axis inclinationangle −10.3 −11.0 −10.5 −10.6 0.5 (adduction direction) [°] Gait cycle[s] 1.06 1.08 1.06 1.07 0.02 Stance ratio [%] 54.7 52.6 54.0 53.8 1.5Direction of knee acceleration vector (at 43.6 38.7 46.6 43.0 3.3 heelcontact) [°] Left Step length [cm] 59.9 57.1 59.0 58.6 1.9 leg Max kneeflexion angle in swing [°] 87.3 85.2 86.6 86.4 1.5 Max knee extensionangle in stance [°] 14.4 14.7 14.5 14.5 0.2 Range of motion of kneejoint [°] 72.9 70.5 72.1 71.9 1.7 Knee flexion angle (immediately afterheel 41.4 37.1 39.9 39.4 3.0 contact) [°] Knee flexion angle (at thetime of toe off) 56.3 55.8 56.2 56.1 0.4 [°] Ankle abduction angle [°]2.6 3.5 2.9 3.0 0.6 Thigh and shank angle [°] 189.8 190.4 190.0 190.10.4 Lower limb functional axis inclination angle −2.3 −2.7 −2.5 −2.5 0.3(abduction direction) [°] Lower limb functional axis inclination angle−11.2 −10.5 −11.0 −10.9 0.5 (adduction direction) [°] Gait cycle [s]1.04 1.13 1.07 1.08 0.06 Stance ratio [%] 53.2 52.9 53.1 53.1 0.2Direction of knee acceleration vector (at 49.4 47 49.3 48.6 1.1 heelcontact) [°]

TABLE 9 Number of steps Standard 1st step 2nd step 3rd step Averagedeviation Right Step length [cm] 57.8 60.7 54.6 57.7 3.0 leg Max kneeflexion angle in swing [°] 94.0 92.6 96.6 94.4 2.1 Max knee extensionangle in stance [°] 18.0 18.3 17.5 17.9 0.4 Range of motion of kneejoint [°] 76.0 74.2 79.1 76.5 2.5 Knee flexion angle (immediately after38.0 39.4 41.2 39.5 1.6 heel contact) [°] Knee flexion angle (at thetime of toe 70.8 70.2 67.2 69.4 2.0 off) [°] Ankle abduction angle [°]13.1 16.9 16.2 15.4 2.0 Thigh and shank angle [°] 171.9 171.8 171.7171.8 0.1 Lower limb functional axis inclination −0.7 −1.2 −2.2 −1.4 0.7angle (abduction direction) [°] Lower limb functional axis inclination−6.9 −7.0 −8.6 −7.5 0.9 angle (adduction direction) [°] Gait cycle [s]1.03 0.98 0.99 1.00 0.03 Stance ratio [%] 53.8 52.3 52.8 52.9 0.8Direction of knee acceleration vector 46.4 44.1 41.2 43.9 2.1 (at heelcontact) [°] Left leg Step length [cm] 45.8 47.3 51.6 48.3 3.0 Max kneeflexion angle in swing [°] 91.0 94.1 91.4 92.2 1.7 Max knee extensionangle in stance [°] 20.1 21.8 21.9 21.3 1.0 Range of motion of kneejoint [°] 70.9 72.3 69.5 70.9 1.4 Knee flexion angle (immediately after41.8 47.0 47.3 45.4 3.1 heel contact) [°] Knee flexion angle (at thetime of toe 60.8 62.5 65.1 62.8 2.2 off) [°] Ankle abduction angle [°]4.8 4.9 3.1 4.3 1.0 Thigh and shank angle [°] 183.4 183.5 182.8 183.20.4 Lower limb functional axis inclination −0.6 0.0 −2.1 −0.9 1.1 angle(abduction direction) [°] Lower limb functional axis inclination −8.9−8.5 −10.3 −9.2 0.9 angle (adduction direction) [°] Gait cycle [s] 0.991.00 0.99 0.99 0.01 Stance ratio [%] 53.9 53.3 53.9 53.7 0.3 Directionof knee acceleration vector 40 43.8 53 45.6 5.5 (at heel contact) [°]

TABLE 10 Number of steps Standard 1st step 2nd step 3rd step Averagedeviation Right Step length [cm] 45.8 41.7 39.5 42.3 3.2 leg Max kneeflexion angle in swing [°] 89.5 92.5 88.5 90.2 2.1 Max knee extensionangle in stance 15.9 14.2 16.8 15.6 1.3 [°] Range of motion of kneejoint [°] 73.6 78.4 71.7 74.5 3.4 Knee flexion angle (immediately after26.8 19.6 22.5 23.0 3.6 heel contact) [°] Knee flexion angle (at thetime of toe 66.7 70.1 70.0 69.0 1.9 off) [°] Ankle abduction angle [°]−1.3 4.9 5.3 3.0 3.7 Thigh and shank angle [°] 172.8 174.4 175.2 174.21.2 Lower limb functional axis inclination 0.6 −0.5 0.0 0.1 0.5 angle(abduction direction) [°] Lower limb functional axis inclination −5.3−6.5 −5.9 −5.9 0.6 angle (adduction direction) [°] Gait cycle [s] 1.091.07 1.07 1.07 0.01 Stance ratio [%] 53.1 55.2 54.2 54.1 1.1 Directionof knee acceleration vector 39 54.6 37.3 43.6 7.8 (at heel contact) [°]Left Step length [cm] 43.4 42.2 44.5 43.4 1.2 leg Max knee flexion anglein swing [°] 84.0 85.1 83.7 84.3 0.8 Max knee extension angle in stance19.5 20.9 22.7 21.0 1.6 [°] Range of motion of knee joint [°] 64.6 64.361.0 63.3 2.0 Knee flexion angle (immediately after 25.2 26.8 27.3 26.41.1 heel contact) [°] Knee flexion angle (at the time of toe 61.5 61.263.6 62.1 1.3 off) [°] Ankle abduction angle [°] 3.1 1.6 0.4 1.7 1.4Thigh and shank angle [°] 179.2 177.6 177.7 178.2 0.9 Lower limbfunctional axis inclination −2.8 −2.5 −5.5 −3.6 1.7 angle (abductiondirection) [°] Lower limb functional axis inclination −6.3 −6.6 −8.0−7.0 0.9 angle (adduction direction) [°] Gait cycle [s] 1.08 1.08 1.061.07 0.01 Stance ratio [%] 55.7 55.7 56.8 56.1 0.7 Direction of kneeacceleration vector 39.6 47.9 53.6 47.0 5.7 (at heel contact) [°]

TABLE 11 Number of steps Standard 1st step 2nd step 3rd step Averagedeviation Right Step length [cm] 47.4 46.9 41.1 45.1 3.5 leg Max kneeflexion angle in swing [°] 73.2 74.0 75.1 74.1 1.0 Max knee extensionangle in stance [°] 7.3 8.7 9.0 8.3 0.9 Range of motion of knee joint[°] 65.9 65.3 66.1 65.8 0.4 Knee flexion angle (immediately after 19.422.0 14.8 18.8 3.7 heel contact) [°] Knee flexion angle (at the time oftoe 56.9 52.2 57.3 55.5 2.8 off) [°] Ankle abduction angle [°] 4.8 2.89.3 5.6 3.3 Thigh and shank angle [°] 175.4 171.4 175.3 174.0 2.3 Lowerlimb functional axis inclination −2.0 −1.1 −3.5 −2.2 1.2 angle(abduction direction) [°] Lower limb functional axis inclination −7.3−6.2 −8.6 −7.4 1.2 angle (adduction direction) [°] Gait cycle [s] 1.221.29 1.37 1.29 0.07 Stance ratio [%] 59.1 61.2 62.6 61.0 1.8 Directionof knee acceleration vector 59.8 59.8 54.1 57.9 2.7 (at heel contact)[°] Left Step length [cm] 39.3 34.1 35.7 36.3 2.7 leg Max knee flexionangle in swing [°] 78.2 73.3 71.9 74.5 3.3 Max knee extension angle instance [°] 13.9 16.7 17.2 15.9 1.8 Range of motion of knee joint [°]64.3 56.6 54.7 58.6 5.1 Knee flexion angle (immediately after 20.6 31.228.5 26.8 5.5 heel contact) [°] Knee flexion angle (at the time of toe51.5 47.2 53.9 50.9 3.4 off) [°] Ankle abduction angle [°] −7.5 −19.1−17.7 −14.8 6.3 Thigh and shank angle [°] 177.3 172.4 172.7 174.2 2.8Lower limb functional axis inclination −6.3 −5.9 −4.4 −5.6 1.0 angle(abduction direction) [°] Lower limb functional axis inclination −10.6−9.0 −11.4 −10.3 1.3 angle (adduction direction) [°] Gait cycle [s] 1.221.43 1.33 1.33 0.11 Stance ratio [%] 60.9 52.7 55.0 56.2 4.2 Directionof knee acceleration vector 58.6 76.9 18.1 51.2 24.6 (at heel contact)[°]

TABLE 12 Number of steps Standard 1st step 2nd step 3rd step Averagedeviation Right Step length [cm] 68.7 62.4 66.6 65.5 4.4 leg Max kneeflexion angle in swing [°] 90.9 91.0 90.9 91.0 0.1 Max knee extensionangle in stance [°] 6.1 6.4 6.2 6.2 0.2 Range of motion of knee joint[°] 84.8 84.7 84.8 84.7 0.1 Knee flexion angle (immediately after 31.031.5 31.2 31.2 0.3 heel contact) [°] Knee flexion angle (at the time oftoe 56.6 51.6 54.9 54.1 3.5 off) [°] Ankle abduction angle [°] 9.2 9.79.4 9.5 0.4 Thigh and shank angle [°] 178.8 179.8 179.1 179.3 0.7 Lowerlimb functional axis inclination 3.1 4.8 3.7 3.9 1.2 angle (abductiondirection) [°] Lower limb functional axis inclination −10.1 −9.2 −9.8−9.7 0.6 angle (adduction direction) [°] Gait cycle [s] 0.90 0.88 0.890.89 0.02 Stance ratio [%] 51.9 49.4 51.0 50.6 1.8 Direction of kneeacceleration vector (at 38.5 38.3 39.7 38.8 0.6 heel contact) [°] LeftStep length [cm] 62.1 65.9 63.4 64.0 2.7 leg Max knee flexion angle inswing [°] 93.1 90.0 92.1 91.6 2.2 Max knee extension angle in stance [°]7.0 7.5 7.2 7.3 0.3 Range of motion of knee joint [°] 86.1 82.5 84.984.3 2.5 Knee flexion angle (immediately after 33.9 33.9 33.9 33.9 0.0heel contact) [°] Knee flexion angle (at the time of toe 52.3 54.6 53.153.5 1.6 off) [°] Ankle abduction angle [°] 8.3 2.0 6.2 5.2 4.4 Thighand shank angle [°] 170.9 170.7 170.9 170.8 0.2 Lower limb functionalaxis inclination 2.8 2.3 2.6 2.6 0.4 angle (abduction direction) [°]Lower limb functional axis inclination −6.2 −6.2 −6.2 −6.2 0.0 angle(adduction direction) [°] Gait cycle [s] 0.88 0.89 0.88 0.88 0.01 Stanceratio [%] 49.4 51.3 50.0 50.3 1.3 Direction of knee acceleration vector(at 44.6 46.6 44.6 45.3 0.9 heel contact) [°]

TABLE 13 Number of steps Standard 1st step 2nd step 3rd step Averagedeviation Right Step length [cm] 43.8 44.1 44.8 44.2 0.5 leg Max kneeflexion angle in swing [°] 91.4 91.9 91.5 91.6 0.3 Max knee extensionangle in stance [°] 19.8 19.3 15.9 18.3 2.1 Range of motion of kneejoint [°] 71.6 72.6 75.6 73.3 2.1 Knee flexion angle (immediately after33.5 35.7 34.5 34.6 1.1 heel contact) [°] Knee flexion angle (at thetime of toe 74.9 75.7 71.1 73.9 2.4 off) [°] Ankle abduction angle [°]−2.3 −3.3 0.5 −1.7 2.0 Thigh and shank angle [°] 170.9 172.9 173.1 172.31.2 Lower limb functional axis inclination −2.9 −5.4 −4.5 −4.3 1.2 angle(abduction direction) [°] Lower limb functional axis inclination −7.8−8.2 −7.2 −7.7 0.5 angle (adduction direction) [°] Gait cycle [s] 1.161.08 1.07 1.10 0.05 Stance ratio [%] 59.6 56.7 55.2 57.2 2.2 Directionof knee acceleration vector (at 61.3 71.8 66 66.4 4.3 heel contact) [°]Left Step length [cm] 43.3 46.4 49.0 46.2 2.8 leg Max knee flexion anglein swing [°] 92.1 93.0 90.4 91.8 1.3 Max knee extension angle in stance[°] 21.4 21.8 21.5 21.5 0.2 Range of motion of knee joint [°] 70.7 71.269.0 70.3 1.2 Knee flexion angle (immediately after 44.0 37.6 35.5 39.04.4 heel contact) [°] Knee flexion angle (at the time of toe 71.8 75.672.7 73.4 2.0 off) [°] Ankle abduction angle [°] −8.1 −6.4 −5.7 −6.7 1.3Thigh and shank angle [°] 174.9 174.4 174.2 174.5 0.3 Lower limbfunctional axis inclination −1.7 −3.4 −3.9 −3.0 1.1 angle (abductiondirection) [°] Lower limb functional axis inclination −4.2 −4.5 −5.8−4.9 0.9 angle (adduction direction) [°] Gait cycle [s] 1.09 1.07 1.101.09 0.02 Stance ratio [%] 56.1 55.2 55.6 55.6 0.5 Direction of kneeacceleration vector (at 60 59.5 61.9 60.5 1.0 heel contact) [°]

TABLE 14 Number of steps Standard 1st step 2nd step 3rd step Averagedeviation Right Step length [cm] 53.5 53.2 53.9 53.5 0.4 leg Max kneeflexion angle in swing [°] 83.5 87.3 87.8 86.2 2.4 Max knee extensionangle in stance [°] 5.5 9.2 8.9 7.8 2.0 Range of motion of knee joint[°] 78.0 78.1 78.9 78.3 0.5 Knee flexion angle (immediately after 30.728.5 27.8 29.0 1.5 heel contact) [°] Knee flexion angle (at the time oftoe 59.2 59.8 60.9 60.0 0.8 off) [°] Ankle abduction angle [°] −2.9 −1.1−2.0 −2.0 0.9 Thigh and shank angle [°] 176.7 177.5 177.3 177.2 0.4Lower limb functional axis inclination 1.5 1.3 2.6 1.8 0.7 angle(abduction direction) [°] Lower limb functional axis inclination −8.0−8.0 −7.7 −7.9 0.1 angle (adduction direction) [°] Gait cycle [s] 0.990.94 0.97 0.97 0.02 Stance ratio [%] 55.1 51.8 51.7 52.8 1.9 Directionof knee acceleration vector 67.1 47.5 55.3 56.6 8.1 (at heel contact)[°] Left Step length [cm] 49.1 54.8 55.5 53.1 3.5 leg Max knee flexionangle in swing [°] 82.0 83.0 84.9 83.3 1.5 Max knee extension angle instance [°] 10.5 13.2 14.9 12.9 2.2 Range of motion of knee joint [°]71.5 69.7 70.0 70.4 1.0 Knee flexion angle (immediately after 33.3 34.433.0 33.6 0.7 heel contact) [°] Knee flexion angle (at the time of toe61.3 63.2 61.0 61.8 1.2 off) [°] Ankle abduction angle [°] 2.7 −0.4 0.50.9 1.6 Thigh and shank angle [°] 183.4 183.7 185.4 184.2 1.1 Lower limbfunctional axis inclination −0.4 −2.1 −3.6 −2.0 1.6 angle (abductiondirection) [°] Lower limb functional axis inclination −6.5 −7.3 −7.2−7.0 0.4 angle (adduction direction) [°] Gait cycle [s] 0.96 0.96 0.970.96 0.01 Stance ratio [%] 53.5 53.5 52.9 53.3 0.4 Direction of kneeacceleration vector 55.3 62.6 55.7 57.9 3.4 (at heel contact) [°]

TABLE 15 Number of steps Standard 1st step 2nd step 3rd step Averagedeviation Right Step length [cm] 50.3 51.4 46.9 49.5 2.4 leg Max kneeflexion angle in swing [°] 78.1 78.9 79.4 78.8 0.6 Max knee extensionangle in stance [°] 13.8 12.8 12.6 13.0 0.6 Range of motion of kneejoint [°] 64.4 66.1 66.8 65.8 1.2 Knee flexion angle (immediately after18.4 22.5 17.4 19.4 2.7 heel contact) [°] Knee flexion angle (at thetime of toe 54.5 56.9 54.0 55.1 1.5 off) [°] Ankle abduction angle [°]4.5 7.9 3.2 5.2 2.4 Thigh and shank angle [°] 180.1 178.3 178.0 178.81.1 Lower limb functional axis inclination 2.1 2.2 1.4 1.9 0.5 angle(abduction direction) [°] Lower limb functional axis inclination −9.9−9.7 −10.7 −10.1 0.6 angle (adduction direction) [°] Gait cycle [s] 1.041.04 1.04 1.04 0.00 Stance ratio [%] 55.3 54.3 54.3 54.6 0.6 Directionof knee acceleration vector 54 64.3 59.5 59.3 4.2 (at heel contact) [°]Left Step length [cm] 57.8 55.2 60.7 57.9 2.8 leg Max knee flexion anglein swing [°] 87.8 89.6 86.7 88.0 1.5 Max knee extension angle in stance[°] 13.6 14.5 19.1 15.7 3.0 Range of motion of knee joint [°] 74.2 75.167.6 72.3 4.1 Knee flexion angle (immediately after 33.2 32.0 34.9 33.41.4 heel contact) [°] Knee flexion angle (at the time of toe 60.5 58.662.7 60.6 2.1 off) [°] Ankle abduction angle [°] 3.1 1.0 1.1 1.7 1.2Thigh and shank angle [°] 180.1 179.5 180.4 180.0 0.5 Lower limbfunctional axis inclination −4.4 −3.8 −4.1 −4.1 0.3 angle (abductiondirection) [°] Lower limb functional axis inclination −9.1 −7.7 −9.0−8.6 0.8 angle (adduction direction) [°] Gait cycle [s] 1.02 1.06 1.081.05 0.03 Stance ratio [%] 55.4 53.7 52.6 53.9 1.4 Direction of kneeacceleration vector 60.8 60.4 65.1 62.1 2.1 (at heel contact) [°]

TABLE 16 Number of steps Standard 1st step 2nd step 3rd step Averagedeviation Right Step length [cm] 50.3 54.2 54.0 52.8 2.2 leg Max kneeflexion angle in swing [°] 82.9 80.6 82.4 82.0 1.2 Max knee extensionangle in stance [°] 13.1 12.5 13.3 13.0 0.4 Range of motion of kneejoint [°] 69.8 68.1 69.1 69.0 0.9 Knee flexion angle (immediately after28.9 25.6 26.1 26.9 1.8 heel contact) [°] Knee flexion angle (at thetime of toe 55.1 55.1 56.6 55.6 0.9 off) [°] Ankle abduction angle [°]−0.2 −0.6 −0.4 −0.4 0.2 Thigh and shank angle [°] 178.7 180.9 181.2180.2 1.4 Lower limb functional axis inclination 2.2 1.5 1.8 1.9 0.4angle (abduction direction) [°] Lower limb functional axis inclination−8.2 −8.2 −8.8 −8.4 0.3 angle (adduction direction) [°] Gait cycle [s]1.07 1.06 1.04 1.06 0.01 Stance ratio [%] 58.3 56.8 55.3 56.8 1.5Direction of knee acceleration vector 65.1 54.8 46.5 55.5 7.6 (at heelcontact) [°] Left Step length [cm] 53.4 55.6 56.4 55.1 1.5 leg Max kneeflexion angle in swing [°] 82.5 86.5 84.5 84.5 2.0 Max knee extensionangle in stance [°] 13.3 10.3 11.8 11.8 1.5 Range of motion of kneejoint [°] 69.2 76.1 72.7 72.7 3.5 Knee flexion angle (immediately after26.0 22.5 22.0 23.5 2.2 heel contact) [°] Knee flexion angle (at thetime of toe 60.2 57.0 59.1 58.7 1.6 off) [°] Ankle abduction angle [°]0.5 −0.3 −1.9 −0.6 1.3 Thigh and shank angle [°] 185.3 184.3 185.7 185.10.7 Lower limb functional axis inclination 4.0 3.1 2.9 3.3 0.5 angle(abduction direction) [°] Lower limb functional axis inclination −7.0−7.8 −8.3 −7.7 0.7 angle (adduction direction) [°] Gait cycle [s] 1.031.04 1.08 1.05 0.02 Stance ratio [%] 53.8 56.4 55.7 55.3 1.4 Directionof knee acceleration vector 42.9 54.9 55.5 51.1 5.8 (at heel contact)[°]

(Reproducibility of Measurement)

Regarding reproducibility of measurement, referring to Table 3, acomparison of level ground gait between measurement dates, there can beseen no significant difference in any of the parameters, andreproducibility can be recognized. Referring to Table 4, a comparisonbetween the measurers, it can be seen that there are significantdifferences between the maximum knee flexion angles, the minimum kneeflexion angles, and the knee flexions at the time of the toe off. Thisis presumably because of a difference in attachment position of themarkers for use in determining the segment coordinate system. Inparticular, the marker of the great trochanter is technically attachedto the outermost point of the great trochanter. However, because thegreat trochanter is a relatively large landmark, misalignment tends tooccur. However, this problem is not specific to the system of thepresent invention, but is a problem that can similarly occur in adifferent system using a marker, e.g., an optical system.

(Quantitative Assessment of Knee OA Symptoms)

Next, the results of measurement of Patient A are taken as an example todescribe the quantitative assessment of knee OA symptoms. Referring toFIG. 30(a), first, it can be seen that the peak value of the flexionangle of the left knee the severity of which is higher is significantlysmaller than that of the healthy persons. This indicates restrictions onknee flexion due to knee pain. While the average value of the maximumknee flexion angles of the healthy persons is 84.9°, the left knee ofPatient A is 72.4°. In addition, there is a large difference in steplength between the right and the left due to knee pain in the left knee.While the ratio of the right and left step lengths (right steplength/left step length) of the healthy group is 1.02±0.08, almost thesame between the right and the left, the right and left ratio of PatientA is 0.79. In addition, similarly due to knee pain in the left knee,there is also a difference in stance ratio between the right and theleft, and its value is also obtained as a measurement result.

(Comparison Between the Patient Group and the Healthy Group)

Tables 17 to 20 described below indicate results of comparisons betweenthe gait parameters of the patient group and the healthy group. TheTables respectively indicate comparisons of the parameters of the rightleg, the left leg, the side with higher severity, and the side withlower severity. Table 2 described above indicates which leg has higherseverity. Regarding the patients and the healthy persons whose severityis comparable between the right and the left, the average values of theright and left legs were used for both the side with higher severity andthe side with lower severity. The p values in the Tables are valuesobtained when an unpaired t-test was conducted.

TABLE 17 Knee OA group Healthy group Average Average (Standard (StandardRight leg deviation) deviation) p-value Step length [cm] 50.7 (8.6) 59.3(4.0) 0.025 Max knee flexion angle 86.4 (6.5) 85.3 (6.8) 0.758 in swing[°] Max knee extension angle 11.2 (3.7) 14.1 (5.6) 0.228 in stance [°]Range of motion of knee 74.3 (5.8) 71.0 (6.6) 0.305 joint [°] Kneeflexion angle 29.8 (7.6) 27.8 (6.2) 0.563 (immediately after heelcontact) [°] Knee flexion angle (at 62.4 (6.8) 61.1 (4.9) 0.668 the timeof toe off) [°] Ankle abduction angle [°] 6.4 (5.4) 8.5 (7.9) 0.520Thigh and shank angle [°] 177.1 (4.5) 182.0 (8.1) 0.145 Lower limbfunctional −0.3 (2.0) −1.7 (2.4) 0.224 axis inclination angle (abductiondirection) [°] Lower limb functional −8.5 (1.9) −7.4 (1.5) 0.207 axisinclination angle (adduction direction) [°] Gait cycle [s] 1.07 (0.10)1.19 (0.08) 0.018 Stance ratio [%] 55.4 (2.8) 54.7 (2.0) 0.569 Anglebetween right 7.4 (5.3) 1.6 (2.8) 0.018 and left knee joint tranjectory[°] Direction of knee 49.9 (9.9) 61.7 (13.1) 0.058 acceleration vector(at heel contact) [°]

TABLE 18 Knee OA group Healthy group Average Average (Standard (StandardLeft leg deviation) deviation) p-value Step length [cm] 50.8 (7.1) 57.5(5.1) 0.048 Max knee flexion angle 87.0 (5.4) 84.5 (5.1) 0.366 in swing[°] Max knee extension angle 13.5 (4.7) 12.6 (3.9) 0.672 in stance [°]Range of motion of knee 72.4 (6.2) 70.9 (6.2) 0.651 joint [°] Kneeflexion angle 33.6 (9.0) 27.7 (7.0) 0.171 (immediately after heelcontact) [°] Knee flexion angle (at 61.1 (5.7) 60.7 (4.9) 0.858 the timeof toe off) [°] Ankle abduction angle [°] 1.5 (5.0) 5.1 (10.1) 0.360Thigh and shank angle [°] 180.1 (4.8) 183.0 (9.6) 0.392 Lower limbfunctional −0.8 (2.7) −3.1 (2.5) 0.092 axis inclination angle (abductiondirection) [°] Lower limb functional −8.4 (2.1) −8.2 (1.2) 0.805 axisinclination angle (adduction direction) [°] Gait cycle [s] 1.06 (0.11)1.19 (0.09) 0.020 Stance ratio [%] 54.3 (1.8) 55.6 (1.8) 0.181 Anglebetween right 7.2 (3.9) 1.0 (2.4) 0.002 and left knee joint tranjectory[°] Direction of knee 54.2 (8.5) 60.3 (9.1) 0.190 acceleration vector(at heel contact) [°]

TABLE 19 Knee OA group Healthy group Average Average (Standard (StandardHigher severity side deviation) deviation) p-value Step length [cm] 50.3(6.1) 58.4 (3.9) 0.007 Max knee flexion angle 85.5 (6.1) 84.9 (5.5)0.843 in swing [°] Max knee extension angle 12.7 (3.8) 13.3 (4.7) 0.766in stance [°] Range of motion of knee 71.8 (6.4) 71.0 (6.0) 0.795 joint[°] Knee flexion angle 31.1 (8.4) 27.7 (6.5) 0.389 (immediately afterheel contact) [°] Knee flexion angle (at 60.9 (6.1) 60.9 (4.0) 0.991 thetime of toe off) [°] Ankle abduction angle [°] 3.9 (4.2) 6.8 (8.9) 0.398Thigh and shank angle [°] 178.8 (5.0) 184.5 (8.0) 0.100 Lower limbfunctional −0.7 (2.1) −2.4 (2.0) 0.126 axis inclination angle (abductiondirection) [°] Lower limb functional −8.6 (1.7) −7.8 (1.0) 0.292 axisinclination angle (adduction direction) [°] Gait cycle [s] 1.06 (0.11)1.19 (0.08) 0.020 Stance ratio [%] 54.9 (2.4) 55.1 (1.4) 0.833 Anglebetween right 7.4 (3.0) 1.3 (2.1) 0.000 and left knee joint tranjectory[°] Direction of knee 55.2 (8.9) 61.0 (10.5) 0.251 acceleration vector(at heel contact) [°]

TABLE 20 Knee OA group Healthy group Average Average (Standard (StandardLower severity side deviation) deviation) p-value Step length [cm] 51.1(8.9) 58.4 (3.9) 0.059 Max knee flexion angle 87.8 (5.5) 84.9 (5.5)0.308 in swing [°] Max knee extension angle 12.0 (4.7) 13.3 (4.7) 0.577in stance [°] Range of motion of knee 74.9 (5.1) 71.0 (6.0) 0.178 joint[°] Knee flexion angle 32.3 (8.4) 27.7 (6.5) 0.247 (immediately afterheel contact) [°] Knee flexion angle (at 62.7 (5.9) 60.9 (4.0) 0.502 thetime of toe off) [°] Ankle abduction angle [°] 3.9 (5.2) 6.8 (8.9) 0.417Thigh and shank angle [°] 178.4 (4.2) 184.5 (8.0) 0.068 Lower limbfunctional −0.3 (2.4) −2.4 (2.0) 0.088 axis inclination angle (abductiondirection) [°] Lower limb functional −8.3 (2.1) −7.8 (1.0) 0.513 axisinclination angle (adduction direction) [°] Gait cycle [s] 1.07 (0.10)1.19 (0.08) 0.019 Stance ratio [%] 54.8 (2.2) 55.1 (1.4) 0.737 Anglebetween right 7.2 (5.4) 1.3 (2.1) 0.014 and left knee joint tranjectory[°] Direction of knee 49.0 (8.9) 61.0 (10.5) 0.024 acceleration vector(at heel contact) [°]

TABLE 21 a_(x) (m/sec²) a_(z) (m/sec²) a_(xz) (m/sec²) Average AverageAverage (Standard (Standard (Standard deviation) p-value deviation)p-value deviation) p-value Healthy group 3.28 2.14 4.03 (0.73) (0.43)(0.54) Knee Leg with 4.18 0.243 1.81 0.149 4.70 0.304 OA higher severity(1.88) (0.43) (1.63) group Leg with 4.77 0.071 1.77 0.084 5.16 0.117lower severity (1.95) (0.38) (1.77)

As a result, among the conventional gait parameters, a significantdifference is observed only in the gait cycle and the step length withsignificance level of 5%. However, regarding the step length, the lowerlimb length largely varies between the patient group and the healthygroup. Therefore, it can be said that a substantive difference ispresent in the gait cycle only. Given the above, it is impossible toearly detect a disease, e.g., knee OA, or quantitatively assess thedegree of progression using the conventional gait parameters only.

In contrast, the knee horizontal trajectory plane angle θ_(xy), a gaitparameter calculated by the gait analysis system and the gait analysismethod according to the present embodiment, exhibits a significantdifference regarding both the right and left legs. In addition, althoughnot exhibiting any significant difference regarding the right leg, theleft leg, and the side with higher severity, the acceleration vectordirection θ_(acc) exhibits a significant difference regarding the sidewith lower severity, enabling quantitative assessment of a disease,e.g., knee OA. The novel gait parameters are reviewed in detail below.

First, the knee horizontal plane trajectory of Patient B whose kneehorizontal plane trajectory angle is the largest is reviewed as anexample. In general, knee OA patients tend to have a reduced kneestability due to a reduction in articular cartilage. The instabilitybecomes particularly a problem at the time of the heel contact at whicha load applies and in the subsequent early stance phase, which is a loadresponse phase. Referring to FIG. 31(d), it can be seen that thedistance between the knee and the original point in the Y-direction issmall at the time of the heel contact and in the early stance phase.This is presumably because the leg is brought closer to the originalpoint, i.e., the gravity center position of the body, in order to makeup for the instability of the knee. In the late stance phase, the loadtends to decrease, and therefore the instability is less problematic. Inthe late stance phase, it is presumed that, in this case, the distancebetween the original point and the swinging knee becomes small inpreparation for the heel contact on the opposite side and the distancewith respect to the standing knee is large. Even the knee horizontalplane trajectory angles of the knee OA patients without knee pain differfrom that of the healthy group. Therefore, it is reasonable to presumethat the knee instability is the cause.

Next, the smaller angle θ_(acc) of the knee acceleration vectordirection of the knee OA patients as compared with the healthy personsis presumably due to an increase in rearward component and a reductionin vertical component of the acceleration vector. The causes of anincrease in rearward component presumably include the generation ofvelocity in the forward direction immediately before the heel contact.In general, knee OA patients tend to have a lower one-leg supportability than healthy persons. This is due to knee pain at the time ofhigh loads or looseness of the knee. As a result of this, it is presumedthat, in order to reduce the time for one leg support, the timing of theheel contact with the swing leg is advanced, the heel contact is madebefore the forward velocity of the swing leg, which was swungconsequently, is reduced, and rearward acceleration occurs as if toapply a brake. As can be seen from FIGS. 30(b) and (c) or Table 20, thismay also be inferred from the fact that the angle θ_(acc) of the kneeacceleration vector direction is rather smaller on the side with lowerseverity than on the side with higher severity.

The reduction in vertical component is presumably due to a reduction inamount of displacement in the vertical direction due to a reduction inknee flexion angle. The knee flexion in the swing phase plays a role toensure a clearance of the foot with respect to the ground. A reductionin knee flexion angle due to knee pain reduces the clearance. As aresult, it is presumed that the movement of the leg in the verticaldirection is reduced, and the velocity and the acceleration in thevertical direction are reduced.

Thus, it was found that angle θ_(acc) in the knee acceleration vectordirection was reduced due to knee OA symptoms including knee pain, kneeinstability, and knee flexion restrictions.

Table 21 described below indicates results of a comparison of theacceleration of the ground coordinate system. The average values and thestandard deviations of the rearward component a_(x), the verticalcomponent a_(z), and their square-root of sum of squares a_(xz)of theacceleration vector of the healthy group and the knee OA patient groupare indicated. In addition, the p values in the Table are values at atime when an unpaired t-test was conducted. It can also be seen from theTable that the values a_(x) and a_(xz) are larger in the patient groupand the value a_(z) is smaller in the patient group.

Heretofore, the description has been given on the basis of theembodiment. However, the present invention is not limited to theaforementioned embodiment, but a change may be properly made within thescope of the claims. For example, in the aforementioned embodiment, anexample of determining the novel gait parameters with regard to a kneejoint was described. However, the present invention is not limitedthereto, but the same parameters may be determined with regard to otherlower limb joints, e.g., an ankle joint. In addition, in theaforementioned embodiment, the acceleration sensors and the angularvelocity sensors are attached to both legs to acquire the gaitparameters of both legs. However, the sensors may be attached to eitherone of the legs to calculate the gait parameters of only one leg.

INDUSTRIAL APPLICABILITY

Thus, according to the present invention, it becomes possible to developthe conventional three-dimensional gait analysis using an accelerationsensor and an angular velocity sensor to provide the gait analysismethod and the gait analysis system that can obtain the novel gaitparameters useful for assessment of the gait action of a subject.

REFERENCE SIGNS LIST

-   1 gait analysis system-   3 sensor unit-   4 marker-   5 processing device-   7 monitor screen-   11 data acquisition portion-   13 sensor posture estimation portion-   15 segment posture computation portion-   17 lower limb posture computation portion-   19 gait parameter computation portion

1.-8. (canceled)
 9. A gait analysis method comprising: attaching atri-axial acceleration sensor and a tri-axial angular velocity sensor tolower limb portions across at least one joint of joints constituting atleast one of lower limbs of a subject; measuring acceleration andangular velocity of each lower limb portion with the tri-axialacceleration sensor and the tri-axial angular velocity sensor duringgait of the subject; calculating a posture of each lower limb portionduring the gait based on the acceleration and the angular velocitymeasured; constructing a three-dimensional model including a motiontrajectory of the at least one joint by coupling lower limb portions ina calculated posture to one another; and calculating an angle of anacceleration vector of the at least one joint at a time of heel contactwith regard to the motion trajectory in a sagittal plane as a gaitparameter.
 10. The gait analysis method according to claim 9, whereinthe at least one joint is a knee joint.
 11. The gait analysis methodaccording to claim 9, wherein the three-dimensional model including themotion trajectory of at least one joint is constructed with regard toeach of right and left lower limbs of the subject.
 12. The gait analysismethod according to claim 10, wherein the three-dimensional modelincluding the motion trajectory of at least one joint is constructedwith regard to each of right and left lower limbs of the subject. 13.The gait analysis method according to claim 11, wherein an approximationstraight line is formed with respect to each of motion trajectories ofright and left joints in a horizontal plane, and an angle formed betweenthe approximation straight lines is calculated as a gait parameter. 14.The gait analysis method according to claim 12, wherein an approximationstraight line is formed with respect to each of motion trajectories ofright and left joints in a horizontal plane, and an angle formed betweenthe approximation straight lines is calculated as a gait parameter. 15.The gait analysis method according to claim 9, wherein a Lissajousfigure of a joint is created from the three-dimensional model, and thegait parameter is calculated based on the Lissajous figure.
 16. The gaitanalysis method according to claim 10, wherein a Lissajous figure of ajoint is created from the three-dimensional model, and the gaitparameter is calculated based on the Lissajous figure.
 17. The gaitanalysis method according to claim 11, wherein a Lissajous figure of ajoint is created from the three-dimensional model, and the gaitparameter is calculated based on the Lissajous figure.
 18. The gaitanalysis method according to claim 12, wherein a Lissajous figure of ajoint is created from the three-dimensional model, and the gaitparameter is calculated based on the Lissajous figure.
 19. The gaitanalysis method according to claim 13, wherein a Lissajous figure of ajoint is created from the three-dimensional model, and the gaitparameter is calculated based on the Lissajous figure.
 20. The gaitanalysis method according to claim 14, wherein a Lissajous figure of ajoint is created from the three-dimensional model, and the gaitparameter is calculated based on the Lissajous figure.
 21. A gaitanalysis system comprising: a tri-axial acceleration sensor and atri-axial angular velocity sensor attached to lower limb portions acrossat least one joint of joints constituting at least one of lower limbs ofa subject, the tri-axial acceleration sensor and the tri-axial angularvelocity sensor measuring acceleration and angular velocity of eachlower limb portion during gait of the subject; a model constructionmeans for calculating a posture of each lower limb portion during thegait based on acceleration and angular velocity measured andconstructing a three-dimensional model including a motion trajectory ofthe at least one joint by coupling lower limb portions in a calculatedposture one another; and a gait parameter calculation means forcalculating an angle of an acceleration vector of the at least one jointat a time of heel contact with regard to the motion trajectory in asagittal plane as a gait parameter.
 22. The gait analysis systemaccording to claim 21, wherein the tri-axial acceleration sensor and thetri-axial acceleration sensor are attached to right and left lower limbsof the subject, and the gait parameter calculation means is configuredto form an approximation straight line with respect to each of motiontrajectories of right and left joints in a horizontal plane andcalculate an angle formed between the approximation straight lines as agait parameter.
 23. The gait analysis system according to claim 21,wherein the parameter calculation means is configured to create aLissajous figure of a joint from the three-dimensional model andcalculate the gait parameter based on the Lissajous figure.
 24. The gaitanalysis system according to claim 22, wherein the parameter calculationmeans is configured to create a Lissajous figure of a joint from thethree-dimensional model and calculate the gait parameter based on theLissajous figure.